CN111859825A

CN111859825A - Method and equipment for simulating unsteady non-pressure flow numerical value with arbitrary flow-solid interface

Info

Publication number: CN111859825A
Application number: CN202010736272.3A
Authority: CN
Inventors: 潘天宇; 李秋实; 苏冠廷; 郑孟宗
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2020-07-28
Filing date: 2020-07-28
Publication date: 2020-10-30
Anticipated expiration: 2040-07-28
Also published as: CN111859825B

Abstract

The present disclosure provides a method and apparatus for simulating unsteady non-compressible flow values involving arbitrary fluid-solid interfaces, the method comprising using a non-physical grid to correctly identify the fluid-solid interface; a fluid-solid boundary condition is applied. The former includes: using a Cartesian grid discrete calculation domain, and using a curve coordinate to describe a fluid-solid interface in a discrete mode; describing an interface-grid relation, defining information of a spatial domain where grid points near an interface are located, and identifying the information as a spatial domain flag of the corresponding grid point; based on the spatial domain flag, the position information of all grid points relative to the fluid-solid interface is defined and identified as the grid line flag of the corresponding grid point. The latter includes: based on an information reconstruction algorithm, adjusting a space discrete template of grid points near the interface according to the grid line flags so as to implant a current fluid-solid interface boundary condition in a space discrete control equation; the time dispersion of the control equation takes a standard time step format. The method disclosed by the invention has good universality and higher calculation efficiency, and does not sacrifice accuracy.

Description

Method and equipment for simulating unsteady non-pressure flow numerical value with arbitrary flow-solid interface

Technical Field

The present disclosure relates to the field of computational fluid mechanics, and in particular, to a fast and accurate numerical simulation method and a computation device suitable for unsteady and non-compressible flow including any fluid-solid interface.

Background

Simulating unsteady flow around an object by Computational Fluid Dynamics (CFD) methods is an important part of many engineering research design efforts. In order to improve the reference value of the calculation simulation result to the actual design application, the shape of the simulated object is often required to be approximately consistent with the real situation, and therefore, the fluid-solid interface in the simulation problems is often complex. At present, the computational power of a computer is greatly improved, a traditional computational fluid mechanics method still needs to construct and generate a computational grid attached to a complex fluid-solid interface, and then a more complicated control equation discrete method is adopted to realize numerical simulation. With the improvement of the simulation requirement, the processed fluid-solid interface has higher geometric complexity, and the two problems result in that the computational resources consumed by the numerical simulation scheme adopting the traditional CFD method are correspondingly improved. Moreover, according to the fluid-solid interfaces in different problems, different grids need to be constructed, and different control equation discrete methods are adopted, so that the numerical simulation scheme has specificity on a flow simulation object and does not have general universality.

The traditional CFD method is adopted to simulate the unsteady flow of the complex flow-solid interface, the consumption of computing resources is high, the universality is not realized, and the CFD method is limited to carry out numerical simulation on the unsteady flow problem containing the complex flow-solid interface to a certain extent.

Disclosure of Invention

To solve or at least alleviate at least one of the above technical problems, the present disclosure provides a numerical simulation method and a computing device suitable for unsteady, non-pressure flows involving arbitrary fluid-solid interfaces.

According to one aspect of the disclosure, a method for simulating a very constant non-pressure flow value including an arbitrary flow-solid interface comprises the following steps:

identifying a fluid-solid interface using a Cartesian grid comprising:

discretely describing a calculation domain of a model problem by using a Cartesian grid, and discretely describing a fluid-solid interface by using a curve coordinate; and

describing an interface-grid relation, defining information of a spatial domain where grid points near an interface are located, and identifying the information as a spatial domain flag of the corresponding grid point; and

based on the spatial domain flag, the position information of all grid points relative to the fluid fixation interface is determined and is marked as grid line flags of the corresponding grid points; and

applying fluid-solid interface boundary conditions, comprising:

according to the grid line flag, performing information detection operation, and adjusting a space discrete template of grid points near the fluid-solid interface so as to implant the boundary condition of the fluid-solid interface in a space discrete control equation; and

and performing time advancing on the flow control equation subjected to the space discrete processing.

According to at least one embodiment of the present disclosure, the adjusting a spatially discrete template of grid points near a fluid-solid interface according to a grid line flag, includes:

and when a certain grid point is in the fluid domain, and the condition that the related grid point contained in the grid point space discrete template is not in the fluid domain exists, detecting the information by adopting an information reconstruction algorithm.

According to at least one embodiment of the present disclosure, the detecting information by using the information reconstruction algorithm includes:

according to the flow field information of the grid points positioned in the fluid domain and the flow field information of the intersection points, carrying out linear extrapolation interpolation along the direction of grid lines to obtain the virtual flow field information of the relevant grid points;

the intersection point is the intersection point of the grid line between the grid point and the related grid point and the fluid-solid interface.

According to at least one embodiment of the present disclosure, the linear extrapolation interpolation uses the mathematical formula: v. of_G＝α_Bv_B+α_Av_A+α_Ev_E；

v_GThe virtual flow field information to be solved is the positive adjacent point or the negative adjacent point; v. of_BFlow field information of the intersection point of the grid line and the fluid-solid interface is obtained; v. of_AFlow field information of the grid point corresponding to the positive neighbor point or the negative neighbor point; v. of_EFlow field information for another grid point located in the fluid domain adjacent to the grid point and located in the opposite direction to the intersection point; alpha is alpha_B,α_AAnd alpha_EAre all interpolation coefficients;

when Δ b.gtoreq.Δ g,

α_E＝0；

when Δ b<At Δ g, α_B＝2，

Δ b is a distance between the grid point and the intersection point along the grid line, Δ g is a distance between the intersection point and a positive neighboring point or a negative neighboring point along the grid line, and Δ e is a distance between the grid point and an adjacent fluid domain grid point along the grid line.

According to at least one embodiment of the present disclosure, the describing the interface-grid relationship, determining the information of the spatial domain where the grid points near the interface are located, and identifying the information as the spatial domain flag of the corresponding grid point includes:

identifying a grid point closest to a discrete point of a flow-solid interface and constructing a grid point set taking the grid point as a center;

calculating the intersection point of the grid line between any two adjacent grid points in the grid point set and the fluid-solid interface;

identifying two grid points corresponding to grid lines with intersection points with the fluid-solid interface; calculating two unit vectors which take the discrete point of the fluid-solid interface as a starting point and respectively take the two grid points as an end point;

respectively dot-product the normal vector at the discrete point of the fluid-solid interface with the two unit vectors, and confirm that the grid point with a larger dot-product result is positioned in the fluid domain and the other grid point is positioned in the solid domain;

and if the intersection point of the grid line and the fluid-solid interface is coincident with a certain grid point, confirming that the grid point coincident with the intersection point is positioned on the fluid-solid interface.

According to at least one embodiment of the present disclosure, performing spatial domain flag identification on the grid points according to the determination result; the spatial domain flag in the fluid domain is identified as constant a, the spatial domain flag in the solid domain is identified as constant B, and the spatial domain flag in the fluid-solid interface is identified as constant C.

According to at least one embodiment of the present disclosure, a grid line flag identifying a grid point based on a spatial domain flag includes:

if the spatial domain flag of a certain grid point is constant A and the spatial domain flag of the positive neighbor of the grid point is constant B, the grid line flag of the grid point is constant a;

if the spatial domain flag of a certain grid point is constant A and the spatial domain flag of the negative neighboring point of the grid point is constant B, the grid line flag of the grid point is constant B;

if the spatial domain flag of a certain grid point is constant A, and the spatial domain flags of the positive neighbor and the negative neighbor of the grid point are both constant A, the grid line flag of the grid point is constant c;

if the spatial domain flag of a certain grid point is constant B, the grid line flag of the grid point is constant d;

if the spatial domain flag of a certain grid point is constant C, the grid line flag of the grid point is constant 0;

spatial dispersion of the control equations at grid points for which the grid line flag is constant a or constant b involves probing the information for grid points that are in the solid domain.

According to at least one embodiment of the present disclosure, the adjusting the spatially discrete template of the grid points near the fluid fixation interface according to the grid line flag includes:

if all the grid line flags are constant c, the spatial discrete format on the grid line flags is a standard discrete format;

if all the grid line flags are constant d, discrete solution of a flow control equation is not needed at the grid point;

if the grid line flags are 0, the grid point is positioned on the fluid-solid interface, and the boundary condition is directly applied; and

if the grid line flag is constant a or constant b, the spatial discrete template comprises grid points of a solid domain, information detection is carried out on the grid points in the solid domain in the spatial discrete template, and virtual flow field information obtained by the information detection is used for spatial discrete of a control equation.

According to at least one embodiment of the present disclosure, further comprising: and performing time propulsion on the flow control equation after the boundary condition of the fluid-solid interface is applied, wherein the time propulsion momentum equation is as follows:

wherein l is 1,2 and 3 are time sub-steps,

γ₁＝8/15，ρ₁＝0，α₁＝8/15；γ₂＝5/12，ρ₂＝-17/60，α₂＝2/15，γ₃＝3/4，ρ₃＝-5/12，α ₃1/3; when l is 1, l-1 is the last physical time layer, and ρ_lH^l-2＝0；

The intermediate velocity field is obtained and the velocity of the medium,

the pressure poisson equation is solved and,

so as to obtain the final speed field,

so as to obtain the pressure field of the gas,

according to another aspect of the disclosure, a computing device includes:

a memory storing execution instructions; and

a processor executing execution instructions stored by the memory to cause the processor to perform the method of any of the preceding claims.

Drawings

The accompanying drawings, which are included to provide a further understanding of the disclosure and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the disclosure and together with the description serve to explain the principles of the disclosure.

Fig. 1 is a schematic flow diagram of a numerical simulation method of the present disclosure.

Fig. 2 is a schematic diagram illustrating a relationship between a fluid-solid interface and a cartesian grid in the numerical simulation method of the present disclosure.

FIG. 3 is a schematic diagram of discrete processing of a fluid-solid interface in a numerical simulation method of the present disclosure.

Fig. 4 is a schematic diagram of spatial domain identification of grid points in the numerical simulation method of the present disclosure.

Fig. 5 is a schematic diagram of grid line identification of grid points in the numerical simulation method of the present disclosure.

Fig. 6a and fig. 6b are schematic diagrams of a linear extrapolation interpolation algorithm in the numerical simulation method of the present disclosure, respectively.

FIGS. 7a, 7b and 7c are schematic diagrams of the application of the numerical simulation method of the present disclosure to a grid with staggered arrangement; FIG. 7a shows an information arrangement of a staggered grid; FIG. 7b illustrates a discrete format adjustment of the sticky item space; fig. 7c shows a discrete format adjustment to the stream item space.

Figure 8 is a schematic cross-sectional view of the geometric arrangement of the rotating cylinders within the cavity.

Fig. 9 is a diagram illustrating the convergence of the error norm size with discrete steps.

Fig. 10 is a schematic diagram of geometrical parameters of a stationary cylindrical circumfluence steady flow field structure.

FIG. 11 is a diagram illustrating the variation of St with Re in the calculation of the cylindrical flow problem by the numerical simulation method according to the present disclosure compared with the standard numerical result of the existing simulation method.

FIG. 12 is a schematic diagram of one exemplary embodiment of a computing device of the present disclosure.

Detailed Description

The present disclosure will be described in further detail with reference to the drawings and embodiments. It is to be understood that the specific embodiments described herein are for purposes of illustration only and are not to be construed as limitations of the present disclosure. It should be further noted that, for the convenience of description, only the portions relevant to the present disclosure are shown in the drawings.

It should be noted that the embodiments and features of the embodiments in the present disclosure may be combined with each other without conflict. The present disclosure will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.

In the field of computational fluid dynamics, the conventional Computational Fluid Dynamics (CFD) simulation of unsteady flow problems including complex flow-solid boundaries is still tedious and time consuming. An Immersed Boundary Method (IBM) is proposed in the industry for realizing fast numerical simulation, and particularly, a Cartesian immersed boundary mixing method (HCIBM) has the advantages of simple and universal source format, good stability, and the like. However, in the method, the force source items introduced by dispersion near the flow-solid interface by means of a proper flow field information reconstruction algorithm are required, and the normal direction and the sag of the local interface are required to be searched, so that the dispersion can be completed in a form of meeting the boundary condition of the interface. Therefore, when flow field information is reconstructed, the HCIBM needs to consume a large part of computing resources for searching the normal direction and the foothold of the local interface, and the operation is equivalent to constructing a "local skin grid", and has no general universality.

The present disclosure seeks to solve or at least alleviate the above technical problem, with the core difficulty of how to apply the correct fluid-solid interface boundary conditions using a non-skin mesh. If this difficulty can be overcome, a constant orthogonal Cartesian grid can be used to simulate an unsteady flow problem involving a fluid-solid interface of arbitrary shape. Thus, the step of constructing the computational grid in the early stage can be omitted, the fastest discrete method of the Cartesian grid control equation can be used, and the general form of the formed method is not changed along with the specific shape of the fluid-solid interface in a specific problem.

According to an aspect of the present disclosure, there is provided a numerical simulation method suitable for unsteady constant non-pressure flow including any fluid-solid interface, referring to a flow diagram of the numerical simulation method of the present disclosure shown in fig. 1, including: identifying a fluid-solid interface using a Cartesian grid; and applying the correct fluid-solid interface boundary conditions.

The method for identifying the fluid-solid interface by using the Cartesian grid comprises the following substeps:

the computational domain of the model problem is described discretely using a cartesian grid, and the fluid-solid interface is described discretely using curvilinear coordinates, that is, a set of discrete points is used to describe the fluid-solid interface. Preferably, the curvilinear distance between two adjacent discrete points approximates the grid size of the cartesian grid used. The computational domains include a fluid domain, a fluid-solid interface, and a solid domain. The cartesian grid employs a cartesian orthogonal coordinate system, and the position information of each grid point is described by coordinates in the cartesian orthogonal coordinate system. The fluid domain refers to a region in the model in a fluid field, the solid domain refers to a region in the model in a non-fluid field (solid non-flowing), and the fluid-solid interface is the interface of the fluid domain and the solid domain, i.e. the geometric surface of the solid in the model.

Describing the interface-grid relation, defining the information of the spatial domain where the grid points near the interface are located, and identifying the information as the spatial domain flag of the corresponding grid point. This step is to process the grid points near the interface, and determine which region of the spatial domain the grid point is located in for each grid point and the relative positional relationship between the discrete points of the fluid-solid interface, thereby identifying the grid points in the fluid domain, the grid points in the solid domain, and the grid points on the fluid-solid interface.

Based on the spatial domain flag, the position information of all grid points relative to the fluid-solid interface is determined, the grid line flag is marked as the grid line flag of the corresponding grid point, and the information of the spatial domain where one grid point and the adjacent points of the grid point along a certain grid line are located is represented.

Applying a fluid-solid interface boundary condition, comprising the following sub-steps:

according to the grid line flag, performing information detection operation, adjusting a space discrete template of grid points near the fluid-solid interface, and implanting the boundary condition of the fluid-solid interface in a space discrete control equation; and

In the implementation of each step of the numerical simulation method disclosed by the invention, in the process of identifying the fluid-solid interface by using the Cartesian grid and correspondingly applying the boundary condition, the geometric characteristics of the fluid-solid interface are not limited, so that the method is a universal complex interface identification algorithm and a boundary condition application algorithm. The overall formed unsteady flow numerical simulation method does not need to generate a specific skin grid according to the complex boundary of a specific simulation object, and has good universality and higher computational efficiency. In the process of applying the boundary conditions of the fluid-solid interface, the normal direction of the local interface does not need to be constructed, and all operations are completely carried out along the direction of a Cartesian grid line. Meanwhile, the method ensures the uniqueness of the flow field property and solves the problems existing in the similar IBM along the grid lines. The key point of improving the calculation efficiency compared with the body-attached grid algorithm is that the effect of any fluid-solid interface on the flow can be processed by using an orthogonal Cartesian grid, and meanwhile, the example checking result shows that the used processing method has consistent calculation accuracy. Compared with the traditional skin grid algorithm, the method disclosed by the invention has good universality and higher calculation efficiency, and the accuracy is not sacrificed.

In an embodiment of the present disclosure, the step of performing information detection operation according to the grid line flag, and adjusting the spatial discrete template of the grid point near the fluid-solid interface specifically includes: when a certain grid point is in the fluid domain, and the related grid point contained in the grid point space discrete template is not in the fluid domain (namely, the flow information is not stored), the information is detected by adopting an information reconstruction algorithm. Wherein a spatially discrete template of a grid point refers to a set of several grid points centered on the grid point. That is to say, in the spatially discrete template where the grid point is located, if there is a case where the grid point is not in the fluid domain in other grid points except the grid point, the information is detected by using the information reconstruction algorithm. The point where information detection is performed is a grid point which is not in the fluid domain.

The meaning of information detection is explained below in terms of the concepts of positive neighbors and negative neighbors. For a grid point at a central position in the spatial discrete template, an adjacent point on a grid line along a positive direction of a certain coordinate is a positive adjacent point of the grid point in the direction, and correspondingly, an adjacent point on a grid line along a negative direction of the certain coordinate is a negative adjacent point of the grid point in the direction. In a Cartesian orthogonal coordinate system of the whole space domain, the directions of Cartesian grid lines are respectively parallel to an x axis, a y axis and a z axis, the positive coordinate directions refer to the positive directions of the x axis, the y axis and the z axis, and the negative directions are opposite. The meaning of the normal adjacent point means that the direction from a certain grid point to the normal adjacent point is consistent with the positive direction of a certain coordinate axis. The meaning of the negative neighboring point means that the direction from a certain grid point to the negative neighboring point is consistent with the negative direction of a certain coordinate axis. It can be understood that a certain grid point has three positive neighbors and three negative neighbors in the three coordinate axis directions, and likewise, the same positive neighbor or negative neighbor corresponds to three related grid points respectively. If a certain grid point is located in the fluid domain and the positive neighboring point or the negative neighboring point of the grid point is located in the solid domain, performing information detection on the positive neighboring point or the negative neighboring point located in the solid domain to obtain virtual flow field information of the positive neighboring point or the negative neighboring point (located in the solid domain) so as to obtain a flow-solid interface boundary condition corresponding to the grid point. The virtual flow field information referred to in the present disclosure is not physical information of flow properties, but virtual information observed when fluid points (grid points located in a fluid domain) meet local boundary conditions at intersection points of the fluid consolidation interfaces, and does not represent actual physical properties thereon. And the virtual information can only be used in the calculation process of the discrete control equation of the corresponding fluid point and cannot be called by other fluid points. Because the same positive neighboring point or negative neighboring point may correspond to a plurality of fluid points, the same positive neighboring point or negative neighboring point may have a plurality of virtual information observed by different fluid points, and the virtual information correspondingly satisfies different boundary conditions.

In one embodiment of the present disclosure, the information detection using the information reconstruction algorithm includes: and performing linear extrapolation interpolation along the direction of the grid lines according to the flow field information of the grid points located in the fluid domain and the flow field information of the intersection points to obtain the virtual flow field information of the relevant grid points. Wherein the intersection point is the intersection point of the grid line between the grid point and the related grid point and the fluid-solid interface. That is, the information detection may be to construct information of corresponding solid-state grid points according to information of fluid-state grid points and fluid-solid boundary points, and the format of the algorithm used is linear extrapolation interpolation along the direction of grid lines.

In an embodiment of the present disclosure, the step of describing the interface-grid relationship, determining information of a spatial domain where grid points near the interface are located, and identifying a spatial domain flag corresponding to a grid point specifically includes: identifying a grid point closest to a discrete point of a flow-solid interface and constructing a grid point set taking the grid point as a center;

Further, performing spatial domain flag identification on the grid points according to the judgment result; the spatial domain flag in the fluid domain is identified as constant a, the spatial domain flag in the solid domain is identified as constant B, and the spatial domain flag in the fluid-solid interface is identified as constant C.

Further, the method also comprises the following steps: if the spatial domain flag of a certain grid point is constant A and the spatial domain flag of the positive neighbor of the grid point is constant B, the grid line flag of the grid point is constant a;

Further, adjusting the spatially discrete template of grid points near the fluid-solid interface according to the grid line flag includes:

In one embodiment of the present disclosure, the flow control equation after the fluid-solid interface boundary condition is applied is time-advanced, and the time-advanced momentum equation is:

wherein l is 1,2 and 3 are time sub-steps,

The intermediate velocity field is obtained and the velocity of the medium,

the pressure poisson equation is solved and,

so as to obtain the final speed field,

so as to obtain the pressure field of the gas,

one embodiment of the numerical simulation method of the present disclosure is given below in conjunction with the accompanying drawings to explain in detail the principles and implementation steps of the present disclosure.

The numerical simulation method of the present disclosure may simulate unsteady flows involving complex fluid-solid interfaces using an orthogonal cartesian grid. The idea of simulating unsteady flow including a complex flow-solid interface by using an orthogonal cartesian grid has been proposed, and a class of methods generally called as an Immersed Boundary Method (IBM) is formed. A technical difficulty in using orthogonal cartesian grids to simulate unsteady flows involving complex fluid-solid interfaces is how to apply the correct fluid-solid interface boundary conditions during flow solution using non-planar grids. The present disclosure breaks this technical difficulty down into two aspects around which the whole technical solution is developed:

1. complex interfaces are identified using cartesian grids and the application of the identification process is not limited to interfaces having certain geometric characteristics. A Cartesian grid complex interface universal recognition algorithm based on the grid line direction is adopted.

2. Flow field information near the interface is reconstructed according to the interface identification result, and the space discrete format of the flow control equation is indirectly adjusted, so that correct boundary conditions of the fluid-solid interface are applied. A Cartesian grid fluid-solid interface information reconstruction algorithm based on the grid line direction is adopted.

The whole technical scheme only adopts the operation in the grid line direction, and does not need to construct the operation of projection and the like in the direction deviating from the grid line (such as the normal direction).

Step 1, discretely describing interface geometry

For an arbitrarily shaped continuous interface, this step may use a set of discrete points { L }It is described mathematically, as shown in FIG. 3; in fig. 3, the thick solid lines represent interfaces, the thin solid lines represent cartesian grids, the open circles represent discrete points of the interfaces, the filled circles represent grid points, and the solid arrows represent normal directions on the interfaces that point to the fluid zones. First { L }The coordinates of the discrete points in (a) in the orthogonal coordinate system defined by the cartesian grid are obtained when the solid shape is modeled at an earlier stage. Assuming that there exists a curvilinear coordinate system, the distance of the curve from the origin at any point thereon is described using the variable s, { L }The curve distance between adjacent points is selected to approximate the size of the cartesian grid used. While traveling upward along the positive direction of the curvilinear coordinate, the fluid zone is to the left of the direction of travel. Therefore, { L }can be establishedDiscrete points in (2)The relationship of the orthogonal coordinates to the curvilinear coordinates of (2):

x＝x(s),y＝y(s) (1)

for arbitrary discrete points L_mIn the vicinity, the relationship in the formula (1) can be described mathematically by a quadratic polynomial:

x(s)＝a_x,ms²+b_x,ms+c_x,m(2)

y(s)＝a_y,ms²+b_y,ms+c_y,m(3)

and the unknown coefficient therein is represented by L_m-1、L_mAnd L_m+1Coordinates of the three points are obtained through fitting. Through such mathematical description, the relevant geometric information at any point on the interface can be directly obtained, for example, the normal vector can be expressed as:

n_x＝-y_s,n_y＝x_s(4)

step 2, describing the relationship between the interface and the numerical grid

The main purpose of this step is to identify grid points near the interface, to determine which grid points are located in the fluid domain, and which grid points are not in the same fluid domain as the aforementioned grid points due to the existence of the interface, and to solve the intersection points of the grid lines and the interface according to the requirement of the whole algorithm. Step 2 { L }Each discrete point in (a) is processed, and the processing is the same for any one discrete point, so that a random discrete point L is used_mExamples are:

referring to fig. 2, in fig. 2, a thick solid line represents an interface, a thin solid line represents a cartesian grid, an open pentagon represents an interface discrete point, a solid circle represents a grid point in a grid point set, an open triangle represents an intersection point of the interface and a grid line, and an arrow of the solid line represents a direction of each vector.

1) Identifying the nearest grid point and constructing a grid point set. Identifying a distance L_mThe nearest grid point (i.e., E in fig. 2)₂₂) Let 9 points centered on the grid point be a set of grid points, and be denoted as { E_ij}_m。

2) And calculatingThe intersection of the grid lines with the interface. With { E_ij}_mThe middle point is an end point, and three line segments are arranged along each coordinate direction. For each line segment, whether the intersection exists with the line segment can be determined by a quadratic equation, and the coordinates of the intersection can also be solved by the equation. E.g. for line segment E₂₁E₂₃Which has an intersection with it of B₂。

3) And processing the line segment having the intersection and contained in { E_ij}_mThe grid points of (a). By line segment E₂₁E₂₃For example, the intersection B is selected₂Directly adjacent grid points on both sides, i.e. E₂₂And E₂₃And, calculating the two unit vectors,

and

and a local normal vector n_m. Then two vector dot products n are calculated_m·e₂₂And n_m·e₂₃. The grid points corresponding to the larger dot product are located in the fluid domain, E in this example₂₃And another point (E)₂₂) Is separated from the fluid domain by an interface. When a certain intersection point coincides with a grid point (e.g. in fig. 2₃₃) And marking the grid point as an interface grid point. When two intersections exist between two adjacent grid points, the two intersections are ignored.

4) After the above processing is completed, if there are unprocessed grid points on the line segment (e.g. fig. 2E)₂₁) Then the spatial domain in which the grid point is located is the same as the spatial domain in which the adjacent grid point located on the same side of the intersection is located (i.e., E)₂₁And E₂₂One spatial domain at the same time).

5) And after all the intersection line segments are processed, if { E }_ij}_mIf there are grid points left unprocessed, the spatial domain where the grid points are located is obtained through the relationship in the formula (4).

The output result of step 2 has a spatial domain flag (i.e. spatial domain identifier) in addition to the intersection coordinates. Where the constant A may be taken to be +10, the constant B may be taken to be-10, and the constant C may be taken to be 0. That is, the spatial domain flag at the grid point in the fluid domain is +10, the spatial domain flag at the grid point in the solid domain is-10, and the spatial domain flag at the grid point in the fluid-solid interface is 0. For the example of fig. 2, the result after marking the spatial domain flag is shown in fig. 4, the thick solid line represents the interface, the thin solid line represents the cartesian grid, the open pentagon represents the discrete points of the interface, the solid circle represents the grid points in the grid point set, and the open triangle represents the intersection points of the interface and the grid lines.

Step 3, obtaining grid line flag (grid line identification) from the spatial domain flag

The process of identifying arbitrary interfaces using cartesian grid tracing has been completed through

steps

1 and 2. Starting from step 3, the information obtained in the first two steps is used to guide the application of the fluid-solid interface boundary conditions. And 3, converting the spatial domain flag (spatial domain identifier) obtained in the step 2 into a grid line flag (grid line identifier) required by the spatial discrete control equation. Each grid point has only one spatial domain flag, but there may be a plurality of grid flag values, each corresponding to a coordinate direction (i.e. each coordinate direction corresponds to a grid mark) representing the relationship between the grid point and its neighboring grid point in that direction. It is now defined that for any grid point, the neighboring points on the grid line along the positive direction of a certain coordinate are the positive neighboring points in the direction, and correspondingly, the neighboring points on the grid line along the negative direction of a certain coordinate are the negative neighboring points in the direction. The constant a may be taken to be-1, the constant b may be taken to be 1, the constant c may be taken to be 10, and the constant d may be taken to be-10. The corresponding relationship between the grid mark values and the spatial domain of the grid point and its positive and negative neighbors is shown in Table 1.

TABLE 1 grid line flags represent the spatial domain in which the grid point and its positive and negative neighbors are located

The grid line flags applicable to the X and Y coordinate directions are referred to as X flags and Y flags, respectively. The grid line flags in each direction are obtained in the same manner, so the specific method for obtaining the grid line flags is exemplified by the Y flag:

1) for grid points with a spatial domain flag of +10, mark the Y flag as +10 first, and then make the following determination:

if the spatial domain flag of the positive neighboring point in the Y direction of the grid point is-10, the Y flag for marking the grid line is-1;

if the grid point Y direction negative neighbor spatial domain flag is-10, then the Y flag marking the grid line is + 1.

2) For grid points with a spatial domain flag of 0, the Y flag marking the grid line is 0.

3) For grid points with a spatial domain flag of-10, the Y flag marking the grid line is-10.

After marking all grid points with the spatial domain flag of-10, if a point in the Y direction of a certain point has a point without the spatial domain flag, the Y flag marking the point is-10, and along the grid line direction, the Y flag marking the point without the spatial domain flag in the way is-10, until a grid point with the spatial domain flag of-10 is encountered.

4) For the points that have not been marked with the Y flag after the above steps, the Y flag is marked as + 10.

After the above steps, the Y flag in the point in fig. 4 is shown in fig. 5, the thick solid line in fig. 5 represents the interface, the thin solid line represents the cartesian grid, the open pentagon represents the discrete points of the interface, the solid circle represents the grid point in the grid point set, and the open triangle represents the intersection point of the interface and the grid line.

Step 4, adjusting the space discrete format of the control equation according to the grid line flag

The flow problem applicable to the present disclosure is a non-constant incompressible flow, the control equation is a non-constant incompressible Navier-Stokes equation, and the non-dimensionalized form using the non-dimensionalized velocity U and the non-dimensionalized length L is:

where U is a dimensionless velocity vector, the X component is U, the Y component is v, and p is ρ U²The dimensionless pressure, t is the dimensionless time of L/U, Re is UL/upsilon is Reynolds number, and rho and upsilon are used for respectively representing the density and the kinematic viscosity of the fluid. For different flow simulation problems, specific values or references for U and L need to be given in advance. When spatial discretization is performed using the second-order central difference format, for any grid point, the spatially discretized basic template contains its neighbors in all coordinate directions and itself.

For any grid point:

if all the grid line flags are +10, the spatial discrete format on the grid line flags is a standard discrete format;

if the grid line flags are-10, discrete solution of the flow control equation is not needed at the point;

if the grid line flags are all 0, then the point is located on the interface, and the boundary condition can be directly applied;

if a grid-line flag is +1 or-1, it represents that the spatially discrete basic template contains non-fluid domain points that do not have flow physics properties thereon that need to be obtained by the spatial reconstruction algorithm.

The essence of the spatial reconstruction algorithm is that the information of corresponding solid domain points is constructed according to the information of flow field grid points and boundary points, and the algorithm format used is linear extrapolation interpolation along the direction of grid lines. Taking solid domain points G as shown in FIGS. 6a and 6b as an example, FIG. 6a is a linear extrapolation interpolation mode of Δ b ≧ Δ G, FIG. 6b is a linear extrapolation interpolation mode of Δ b < Δ G, thin solid lines indicate Cartesian grids, solid circles indicate grid points located in the fluid domain, open triangles indicate intersections of the interface with the grid lines, open circles indicate grid points located in the solid domain, arrows perpendicular to the grid lines indicate the magnitude of a scalar quantity of the fluid property, solid line arrows indicate physical information of the flow property on the fluid domain or the boundary, dashed line arrows indicate virtual information of the flow property reconstructed in the solid domain, and dashed lines connecting the arrows indicate the interpolation operation. The basic mathematical form of the spatial reconstruction algorithm is as follows:

v_G＝α_Bv_B+α_Av_A+α_Ev_E, (7)

v_Gvirtual flow field information of a positive neighboring point or a negative neighboring point; v. of_BFlow field information of the intersection point of the grid line and the fluid-solid interface is obtained; v. of_AFlow field information of the grid point corresponding to the positive neighbor point or the negative neighbor point; v. of_EFlow field information for another grid point located in the fluid domain adjacent to the grid point; alpha is alpha_B,α_AAnd alpha_EAre all interpolation coefficients;

when Δ b ≧ Δ g (FIG. 6a),

when Δ b<Δ g (FIG. 6b), α_B＝2，

Such coefficient setting can ensure the numerical stability of the spatial reconstruction algorithm. It should be additionally noted that the extrapolation interpolation itself is not proposed for the first time, but is not used for the first time, but the special innovation of the patent lies in how to look at and subsequently use the information v constructed by the spatial reconstruction algorithm_G. In the previous method, though v_GNot in the fluid domain itself, but still considered as physical information of the flow properties at that point, is equivalent to the flow field extending inward of the fluid-solid interface. The constructed information is not physical information of flow property, but virtual information observed by a fluid point to meet local boundary conditions on a point B, is exactly positioned on the point G in order to keep the standard of a numerical discrete format, and does not represent an actual object on the point GThe physical property, and the virtual information can only be used in the process of discrete control equation on the corresponding fluid point, and can not be called by other flow field points. Therefore, a plurality of pieces of virtual information observed by different flow field points can be simultaneously arranged on the G point, and the virtual information correspondingly meets different boundary conditions. Therefore, the spatial reconstruction algorithm solves the problem that the prior algorithm based on the grid line direction does not meet the uniqueness of the flow field property. This spatial reconstruction algorithm will be referred to as information detection based on its basic features.

Therefore, when a certain grid line flag is +1 or-1 for any grid point, the information detection is used to acquire the virtual information on the non-fluid domain point in the basic template with the spatial dispersion, thereby completing the spatial dispersion of the control equation. Since the flow field information is arranged in a staggered arrangement manner in some CFD algorithms, as shown in fig. 7a, the specific application is more complicated than the use of a co-located arrangement manner (i.e., all variables are stored at the same location) (the information acquisition in steps 1 to 3 only needs to be repeated for different flow field properties, and no special processing is required). Thus, specific applications will be developed for use on staggered grids, including methods of use on co-located grids.

As shown in fig. 7b, in-square viscosity item

Examples are:

A₁point: the X flag and the Y flag are both 0 and are positioned on the fluid-solid interface, the information of the upper flow field is directly determined according to the boundary condition of the fluid-solid interface, and the flow control equation does not need to be solved;

A₂point: the X flag is +10 and the Y flag is +1, and the negative neighboring point G in the Y direction is determined₁The virtual flow field information is acquired by information detection along the direction of a y grid line;

A₃point: the X flag and the Y flag are both +1, and the negative adjacent point G in the X and Y directions is determined₁And G₂The virtual flow field information on the non-fluid domain points is obtained by information detection along the direction of the y grid lines.

The processing method for all the terms of the control equation in the co-located grid is also summarized above. For the staggered grid, the handling of stream items needs to be specified. As shown in fig. 7c, the neutron terms in the x-direction momentum equation

For example. The following three cases also exist in the special discrete format of the fluid domain points near the fluid-solid interface (only the uv information acquisition case on one side is discussed, and the case on the other side is the same):

for A₁The dot, Y flag is +10, and the corresponding dot in the positive direction of Y, X flag is-1 (E)₁Dots) and-10 (G)₁Dots) such that G₁Virtual v information on a point is represented by E₁Detecting information to obtain A₁Spatial dispersion of (a).

For A₂The dot, Y flag is-1, and the corresponding dot in the positive direction of Y, X flag is-10 (G)₁Dots) and-10 (G)₂Point), at this time, information reconstruction is not carried out, and speed information u and v at the intersection point of the Y grid line and the interface are directly brought into the discrete template to complete space dispersion.

For A₃The dot, Y flag is-1, and the corresponding dot in the positive direction of Y, X flag is-10 (G)₃Dots) and +1 (E)₃Dots) such that G₃Virtual v information on a point is represented by E₃Performing information detection to obtain G₄Virtual u information on the point is represented by A₃Performs information detection to obtain, thereby completing A₃Spatial dispersion of (a).

In fig. 7a to 7c, squares represent storage locations of u, diamonds represent storage locations of v, circles represent storage locations of p, solid symbols represent grid points located in a fluid domain, open symbols represent grid points located in a solid domain, black arrows represent information detection operations, which are initiated by grid points at the tail to reconstruct virtual information pointing to a non-fluid point, and crosses represent locations where u and v information are stored in co-location during discretization.

By the above operation, the required velocity boundary conditions can be imposed in the discrete process of the control equation. In this patent, however, as the speed boundary condition is applied, the pressure boundary condition is implicitly satisfied directly therein, without the discretization of the pressure term taking into account the pressure boundary condition of the extrasolid interface.

Step 5, performing time advancing on the flow control equation subjected to the spatial dispersion treatment

This step can be implemented using currently mature algorithms, one possible implementation of which is now described. The N-S equation can be solved by adopting a time stepping method, the time dispersion of the convection term and the viscosity term is respectively in a three-order R-K format and a Crank-Nicolson format, and the space dispersion format is a second-order central difference format. The whole N-S equation time advancing process is as follows:

1. time-push momentum equation:

wherein l is 1,2 and 3 are time sub-steps,

γ₁＝8/15,ρ₁＝0,α₁＝8/15；γ₂＝5/12,ρ₂＝-17/60,α₂＝2/15；γ₃＝3/4,ρ₃＝-5/12,α ₃1/3. When l is 1, l-1 is the last physical time layer, and ρ_lH^l-2＝0。

2. Obtaining an intermediate velocity field:

3. solving pressure poisson equation

4. Obtaining the final velocity field

5. To obtain a pressure field

In summary, the numerical simulation method of the present disclosure can be summarized as two major steps and five minor steps; 1, correctly identifying the fluid-solid interface by using a Cartesian grid; 2. the fluid-solid boundary conditions are correctly applied. The former includes: the method comprises the following steps that 1, a calculation domain of a model problem is discretely described by using a Cartesian grid, and a fluid-solid interface is discretely described by using a curve coordinate; describing an interface-grid relation, acquiring a spatial domain flag of a grid point near an interface, and describing spatial domain information of the corresponding grid point; and 1c, converting the spatial domain flag into a grid line flag, and describing the position information of the corresponding grid point and the adjacent points relative to the fluid-solid interface. The latter includes: based on an information reconstruction algorithm with good qualitative performance, adjusting a space discrete template of grid points near an interface according to grid line flags, and performing information detection operation, so that a current fluid-solid interface boundary condition is implanted in a space discrete control equation; time dispersion of the control equation is performed using a standard time step format. In the implementation of the above steps, in the process of identifying the complex interface by using the cartesian grid and correspondingly applying the boundary condition, the geometric characteristics of the interface are not limited, so that the method is a general complex interface identification algorithm and boundary condition application algorithm. The overall formed unsteady flow numerical simulation method does not need to generate a specific skin grid according to the complex boundary of a specific simulation object, and has good universality and higher computational efficiency. Meanwhile, as mentioned earlier, the whole technical scheme only adopts the operation in the grid line direction, and does not need to construct the operation of projection and the like deviating from the grid line direction (such as the normal direction), thereby saving the computing resource. The following will provide precision checking and accuracy checking of the entire numerical simulation algorithm. The key to improving computational efficiency compared to the skin-mesh algorithm is that the effect of any fluid-solid interface on flow can be processed using orthogonal cartesian meshes.

Checking the numerical precision:

the present disclosure uses a two-dimensional in-cavity rotating cylinder example to check the numerical accuracy of the submerged boundary method. The computational object of the example is an unsteady flow process induced by a cylinder rotating in a cavity, and the geometric arrangement of the computational domain and boundary conditions is shown in fig. 8. The reynolds number of the flow, Re, is 200, the length scale used for non-dimensionalization is D, and the linear velocity scale is the maximum value of the rotational linear velocity of the cylindrical surface. Let the rotation angle α of the cylinder be:

wherein tau is_c＝π²The rotation period of the cylinder. The angular velocity ω of the cylindrical rotational motion is:

the fixed Curian number is C ═ Δ t/Δ x ═ π²And/16, selecting a space step sequence as Δ x, 1/15,1/25,1/45,1/75 and 1/225. Take several examples of the same time t ═ τ_cThe flow field of (1) is accurately solved by taking the result of the densest grid as an accurate solution, other flow fields are respectively compared with the accurate solution flow field to obtain the error of the speed u in the x direction, and the N is obtained by calculating through the following formula²L of the grid error field_qNorm value

The convergence of the error norm of the calculated result with the discrete step length is shown in fig. 9, and the convergence rate is second order, so the whole numerical simulation method has second order numerical precision.

Checking the accuracy of the algorithm:

the present disclosure will check the accuracy of the proposed immersive boundary method using the stationary cylindrical streaming algorithm. Firstly, checking the structure parameter (see fig. 10) and the velocity distribution parameter of the steady flow field of the cylindrical streaming when the Re is 25, and comparing the structure parameter with the existing standard experiment and numerical value results (see table 2), which shows that the results obtained by the numerical value simulation method disclosed by the invention are quite consistent with the results. In fig. 10, L denotes a separation vortex length; a, b represent the position of the separation vortex nucleus; w represents separation vortex width; θ represents the separation angle. Then, aiming at the unsteady flow simulation result of the standing cylindrical streaming under higher Reynolds number (Re is more than or equal to 50 and less than or equal to 200), the Stewart number St (see figure 11) obtained by comparing the calculation results of the method disclosed by the invention and other methods is also matched.

Table 2 comparison of the results of calculation of stationary cylindrical flow field (Re 25) structure

From the above verification results, the numerical simulation method disclosed by the invention can obtain a result with high accuracy for numerical simulation of both steady and unsteady flow.

According to another aspect of the present disclosure, referring to the schematic view of a computing device of one embodiment of the present disclosure shown in fig. 12, the computing device includes: a communication interface 1000, a memory 2000, and a processor 3000. The communication interface 1000 is used for communicating with an external device to perform data interactive transmission. The memory 2000 has stored therein a computer program that is executable on the processor 3000. The processor 3000 implements the method in the above-described embodiments when executing the computer program. The number of the memory 2000 and the processor 3000 may be one or more.

The memory 2000 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

If the communication interface 1000, the memory 2000 and the processor 3000 are implemented independently, the communication interface 1000, the memory 2000 and the processor 3000 may be connected to each other through a bus to complete communication therebetween. The bus may be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, or the like. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of illustration, only one thick line is shown, but this does not represent only one bus or one type of bus.

Optionally, in a specific implementation, if the communication interface 1000, the memory 2000, and the processor 3000 are integrated on a chip, the communication interface 1000, the memory 2000, and the processor 3000 may complete communication with each other through an internal interface.

Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and the scope of the preferred embodiments of the present disclosure includes other implementations in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the implementations of the present disclosure. The processor performs the various methods and processes described above. For example, method embodiments in the present disclosure may be implemented as a software program tangibly embodied in a machine-readable medium, such as a memory. In some embodiments, some or all of the software program may be loaded and/or installed via memory and/or a communication interface. When the software program is loaded into memory and executed by a processor, one or more steps of the method described above may be performed. Alternatively, in other embodiments, the processor may be configured to perform one of the methods described above by any other suitable means (e.g., by means of firmware).

The logic and/or steps represented in the flowcharts or otherwise described herein may be embodied in any readable storage medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions.

For the purposes of this description, a "readable storage medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the readable storage medium include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable read-only memory (CDROM). In addition, the readable storage medium may even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via for instance optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in the memory.

It should be understood that portions of the present disclosure may be implemented in hardware, software, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on data information, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.

It will be understood by those skilled in the art that all or part of the steps of the method implementing the above embodiments may be implemented by hardware instructions associated with a program, which may be stored in a readable storage medium, and when executed, includes one or a combination of the steps of the method embodiments.

In addition, each functional unit in the embodiments of the present disclosure may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a separate product, may also be stored in a readable storage medium. The storage medium may be a read-only memory, a magnetic or optical disk, or the like.

In the description herein, reference to the description of the terms "one embodiment/mode," "some embodiments/modes," "example," "specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment/mode or example is included in at least one embodiment/mode or example of the application. In this specification, the schematic representations of the terms used above are not necessarily intended to be the same embodiment/mode or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments/modes or examples. Furthermore, the various embodiments/aspects or examples and features of the various embodiments/aspects or examples described in this specification can be combined and combined by one skilled in the art without conflicting therewith.

Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, "plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.

It will be understood by those skilled in the art that the foregoing embodiments are merely for clarity of illustration of the disclosure and are not intended to limit the scope of the disclosure. Other variations or modifications may occur to those skilled in the art, based on the foregoing disclosure, and are still within the scope of the present disclosure.

Claims

1. A method for simulating unsteady non-pressure flow numerical value comprising an arbitrary fluid-solid interface is characterized by comprising the following steps:

identifying a fluid-solid interface using a Cartesian grid comprising:

applying fluid-solid interface boundary conditions, comprising:

2. The numerical simulation method of claim 1, wherein performing information probing operations to adjust the spatially discretized templates of grid points near the fluid-solid interface according to the grid line flags comprises:

3. A numerical simulation method according to claim 2, wherein the detecting information using an information reconstruction algorithm comprises:

4. A numerical simulation method according to claim 3, wherein the linear extrapolation interpolation uses the mathematical formula: v. of_G＝α_Bv_B+α_Av_A+α_Ev_E；

when Δ b.gtoreq.Δ g,

α_E＝0；

when Δ b<At Δ g, α_B＝2，

5. The numerical simulation method of claim 1, wherein the information describing the interface-grid relationship and specifying the spatial domain in which the grid points near the interface are located is identified as the spatial domain flag corresponding to the grid point, comprising:

6. A numerical simulation method as set forth in claim 5, wherein the grid points are identified by spatial domain flags according to the determination result; the spatial domain flag in the fluid domain is identified as constant a, the spatial domain flag in the solid domain is identified as constant B, and the spatial domain flag in the fluid-solid interface is identified as constant C.

7. A numerical simulation method according to claim 6, further comprising:

8. The numerical simulation method of claim 7, wherein the adjusting the spatially discrete templates of grid points near the fluid-solid interface according to the grid line flags comprises:

9. A numerical simulation method according to any one of claims 1 to 8, further comprising: and performing time propulsion on the flow control equation after the boundary condition of the fluid-solid interface is applied, wherein the time propulsion momentum equation is as follows:

wherein l is 1,2 and 3 are time sub-steps,

γ₁＝8/15，ρ₁＝0，α₁＝8/15；γ₂＝5/12，ρ₂＝-17/60，α₂＝2/15，γ₃＝3/4，ρ₃＝-5/12，α₃1/3; when l is 1, l-1 is the last physical time layer, and ρ_lH^l-2＝0；

The intermediate velocity field is obtained and the velocity of the medium,

the pressure poisson equation is solved and,

so as to obtain the final speed field,

so as to obtain the pressure field of the gas,

10. a computing device, comprising:

a memory storing execution instructions; and

a processor executing execution instructions stored by the memory to cause the processor to perform the method of any of claims 1 to 9.