CN110287026A - Efficient implicit time propulsion method based on high accurate scheme and local airflow variable - Google Patents
Efficient implicit time propulsion method based on high accurate scheme and local airflow variable Download PDFInfo
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Abstract
The invention discloses a kind of efficient implicit time propulsion method based on high accurate scheme and local airflow variable, include the following steps: step 1, simultaneously subdivision obtains grid block to given calculating grid, and the control unit minimum right-hand vector of grid block is calculated using interior loop iteration；Step 2, the control unit minimum right-hand vector based on grid block corrects inner iteration virtual time step-length；Step 3, revised inner iteration virtual time step-length is substituted into the discrete equation that interior loop iteration solves the time term of governing equation, until completing the propulsion of a real time step；Step 4, step 1~3 are repeated, until the physical time for completing setting promotes.Robustness of the invention is compared with the traditional method, and in calculating process, maximum allowable CFL condition number generally promotes magnitude or more, demonstrates the robustness of this technology；The computational efficiency of this technology is compared with the traditional method, and forecasting efficiency generally promotes magnitude or more, demonstrates the forecasting efficiency of this technology.
Description
Technical field
The present invention relates to the technical fields such as Fluid Mechanics Computation and applied mathematics, especially a kind of to be based on high accurate scheme
With the efficient implicit time propulsion method of local airflow variable.
Background technique
High-precision Large-scale parallel computing is one of the Main way of the following Fluid Mechanics Computation application, and the big rule of high-precision
It is the important method for coping with complex mesh in practical problem that implicit time in mould parallel computation, which promotes,.It is maximum in complex mesh
Grid control unit volume and the ratio between minimum volume can achieve 109More than, so that using identical CFL condition number iteration
When, the ratio between local time stepping reaches 109Even higher, this constitutes serious choose to the high-precision Large-scale parallel computing of robust
War.Moreover, the grid slenderness ratio in complex mesh can achieve 1000 or more, it is that high-precision Large-scale parallel computing is another great
Challenge.
Currently, in terms of implicit time propulsion, implicit dual time-stepping method is generally used.This method combination second order spatial from
Scattered format achieves extensively successfully application.But for high order spatial discrete scheme, this method will appear in complicated applications
Problem: showing as the inadequate robust of internal layer iteration, need to significantly limit the real time step of propulsion, has severely impacted calculating effect
Rate.
Summary of the invention
The technical problems to be solved by the present invention are: in view of the above problems, providing a kind of based on high accurate scheme
With the efficient implicit time propulsion method of local airflow variable.
The technical solution adopted by the invention is as follows:
A kind of efficient implicit time propulsion method based on high accurate scheme and local airflow variable, includes the following steps:
Step 1, it gives calculating grid and subdivision obtains grid block, the control unit of grid block is calculated using interior loop iteration
Minimum right-hand vector；
Step 2, the control unit minimum right-hand vector based on grid block corrects inner iteration virtual time step-length；
Step 3, revised inner iteration virtual time step-length is substituted into the time term that interior loop iteration solves governing equation
Discrete equation, until complete a real time step propulsion；
Step 4, step 1~3 are repeated, until the physical time for completing setting promotes.
Further, the calculating of the control unit minimum right-hand vector amendment inner iteration virtual time step-length based on grid block is public
Formula is as follows:
Δτ*=max [(RB-min/R0)1.0/power,threshold]*Δτ；
In formula, Δ τ*It is revised inner iteration virtual time step-length；Δ τ indicates the inner iteration virtual time step before amendment
It is long；RB-minIt is the control unit minimum right-hand vector of grid block；R0It is the control unit right-hand vector when ground grid；Power is setting
Modified index；Threshold is the correction threshold of setting.
Further, the modified index power set is 0.5~6.0.
Further, for the relatively large grid block of control unit right-hand vector difference, the modified index power's of setting
Value is relatively small.
Further, the correction threshold threshold set is 0.01~1.0.
Further, for the relatively large grid block of control unit right-hand vector difference, the correction threshold of setting
The value of threshold is relatively small.
Further, the establishment process of the discrete equation of the time term of the governing equation are as follows:
(1) governing equation is discrete using high order spatial format, half discrete form for obtaining governing equation is as follows:
In formula, Q is conservation variable, H and HvRespectively without viscous and sticky flux；All remainders for remembering governing equation are R
(Q)。
(2) virtual time inverse is introduced, difference is discrete after carrying out 3 points of second order accuracy to the time term of governing equation, obtain
The discrete equation of the time term of the governing equation is as follows:
In formula, p indicates that physics time step, Δ t indicate that real time step, m indicate that virtual time promotes step number, Δ τ table
Show virtual time step-length.
Further, described that revised inner iteration virtual time step-length is substituted into interior loop iteration solution governing equation
The process of the discrete equation of time term are as follows:
(1) using the nothing of the discrete equation left end for the time term for calculating governing equation with cell centered scheme windward glue flux and
Sticky flux obtains the discrete equation expansion of the time term of governing equation:
In formula, Av,Bv,CvIndicate the coefficient matrix obtained by sticky flux derivation, δ+And δ-It is operator windward；
(2) D is enabled,It is diagonal matrix, lower triangular matrix and upper triangular matrix respectively, then has:
(3) it enablesThen the discrete equation expansion of the time term of governing equation is similar to as follows
Equation:
LD-1UδQm=R (Qm)；
(4) it takes
Then have
In formula,Expression A, the spectral radius of B, C, | Av,j|,|Bv,k|,|Cv,l| indicate these three viscosity
One norm of matrix；
(5) by LD-1UδQm=R (Qm) resolve into three formula forms:
(6) first in step (5) and third operator are solved with chasing method, the solution of second operator only needs simply
Scalar invert, until governing equation time term discrete equation mean residual drop two magnitudes, complete a physical time
The propulsion of step-length.
In conclusion by adopting the above-described technical solution, the beneficial effects of the present invention are:
Robustness of the invention is compared with the traditional method, and in calculating process, maximum allowable CFL condition number generally promotes one
More than magnitude, demonstrate the robustness of this technology；The computational efficiency of this technology is compared with the traditional method, and forecasting efficiency is generally promoted
More than one magnitude, demonstrate the forecasting efficiency of this technology.
Detailed description of the invention
In order to illustrate the technical solution of the embodiments of the present invention more clearly, below will be to needed in the embodiment attached
Figure is briefly described, it should be understood that the following drawings illustrates only certain embodiments of the present invention, therefore is not construed as pair
The restriction of range for those of ordinary skill in the art without creative efforts, can also be according to this
A little attached drawings obtain other relevant attached drawings.
Fig. 1 is the process of the efficient implicit time propulsion method of the invention based on high accurate scheme and local airflow variable
Block diagram.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that described herein, specific examples are only used to explain the present invention, not
For limiting the present invention, i.e., described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is logical
The component for the embodiment of the present invention being often described and illustrated herein in the accompanying drawings can be arranged and be designed with a variety of different configurations.
Therefore, claimed invention is not intended to limit to the detailed description of the embodiment of the present invention provided in the accompanying drawings below
Range, but be merely representative of selected embodiment of the invention.Based on the embodiment of the present invention, those skilled in the art are not having
Every other embodiment obtained under the premise of creative work is made, shall fall within the protection scope of the present invention.
Feature and performance of the invention are described in further detail with reference to embodiments.
Embodiment 1
A kind of efficient implicit time propulsion method based on high accurate scheme and local airflow variable provided in this embodiment,
As shown in Figure 1, including the following steps:
Step 1, it gives calculating grid and subdivision obtains grid block, the control unit of grid block is calculated using interior loop iteration
Minimum right-hand vector；
Step 2, the control unit minimum right-hand vector based on grid block corrects inner iteration virtual time step-length；
Step 3, revised inner iteration virtual time step-length is substituted into the time term that interior loop iteration solves governing equation
Discrete equation, until complete a real time step propulsion；
Step 4, step 1~3 are repeated, until the physical time for completing setting promotes.
In the present embodiment, for the governing equation under generalized curvilinear coordinate, the time term of the governing equation from
Dissipate the establishment process of equation are as follows:
(1) governing equation is discrete using high order spatial format, half discrete form for obtaining governing equation is as follows:
In formula, Q is conservation variable, H and HvRespectively without viscous flux and sticky flux；Note governing equation all remainders be
R(Q)。
(2) in order to solve Non―steady Problem, virtual time inverse is introduced, second order accuracy is carried out to the time term of governing equation
Difference is discrete after 3 points, and the discrete equation for obtaining the time term of the governing equation is as follows:
In formula, p indicates that physics time step, Δ t indicate that real time step, m indicate that virtual time promotes step number, Δ τ table
Show virtual time step-length.
By the discrete equation of the time term of the governing equation along virtual time direction line, following equation is obtained:
For the Large-scale parallel computing of high accurate scheme, realizes that the efficient implicit time of robust promotes, interior circulation must be used
The control unit minimum right-hand vector for iterating to calculate grid block, the control unit minimum right-hand vector amendment inner iteration based on grid block are empty
Pseudotime step-length, i.e., on amendment type in virtual time step delta τ, calculation formula is as follows:
Δτ*=max [(RB-min/R0)1.0/power,threshold]*Δτ；
In formula, Δ τ*It is revised inner iteration virtual time step-length；Δ τ indicates the inner iteration virtual time step before amendment
It is long；RB-minIt is the control unit minimum right-hand vector of grid block, it should be noted that RB-minIt is the minimum right end in each grid block
, each grid block both corresponds to a R after parallel subdivisionB-min；R0It is the control unit right-hand vector when ground grid；Power is
The modified index of setting；Threshold is the correction threshold of setting.The control unit being calculated by loop iteration in introducing
Minimum right-hand vector corrects the virtual time step-length of interior loop iteration, greatly improves the robustness of internal layer iteration, relax simultaneously
The limitation of step-length is promoted to physical time, that computational efficiency can generally promote a magnitude is even higher.
Wherein, the modified index power set is 0.5~6.0.Further, for control unit right-hand vector difference phase
To biggish calculating grid, the value of the modified index power of setting is relatively small.
Wherein, the correction threshold threshold set is 0.01~1.0.Further, poor for control unit right-hand vector
Not relatively large calculating grid, the value of the correction threshold threshold of setting are relatively small.
The time term that revised inner iteration virtual time step-length is substituted into interior loop iteration solution governing equation
The process of discrete equation are as follows:
(1) using the nothing of the discrete equation left end for the time term for calculating governing equation with cell centered scheme windward glue flux and
Sticky flux obtains the discrete equation expansion of the time term of governing equation:
In formula, Av,Bv,CvIndicate the coefficient matrix obtained by sticky flux derivation, δ+And δ-It is operator windward；
(2) D is enabled,It is diagonal matrix, lower triangular matrix and upper triangular matrix respectively, then has:
(3) it enablesThen the discrete equation expansion of the time term of governing equation is similar to as follows
Equation:
LD-1UδQm=R (Qm)；
(4) it takes
Then have
In formula,Expression A, the spectral radius of B, C, | Av,j|,|Bv,k|,|Cv,l| indicate these three viscosity
One norm of matrix；
(5) by LD-1UδQm=R (Qm) resolve into three formula forms:
(6) first in step (5) and third operator are solved with chasing method, the solution of second operator only needs simply
Scalar invert, until governing equation time term discrete equation mean residual drop two magnitudes, complete a physical time
The propulsion of step-length.
Using the efficient implicit time propulsion method of the invention based on high accurate scheme and local airflow variable, carry out big
The unsteady solver of the parallel dual-time scale of scale, it is only necessary to complete following work:
(1) it gives calculating grid and subdivision obtains grid block, the control unit of grid block is calculated most using interior loop iteration
Small right-hand vector.It should be noted that control unit minimum right-hand vector R hereB-minIt is the minimum value in each grid block, parallel
Each grid block both corresponds to a minimum right-hand vector R after subdivisionB-min。
(2) calculation formula Δ τ is used*=max [(RB-min/R0)1.0/power, threshold] * Δ τ amendment inner iteration void
Pseudotime step-length；Correct the minimum control of each grid block after containing parallel subdivision in the equation of inner iteration virtual time step-length
Equation right-hand vector R processedB-min, therefore, even if original solution code has solved governing equation right-hand vector, it is still to expand each net of solution
The minimum governing equation right-hand vector R of lattice subdivision blockB-min。
(3) by revised inner iteration virtual time step-length substitute into loop iteration solve governing equation time term from
Equation is dissipated, until completing the propulsion of a real time step；
(4) step 1~3 are repeated, until the physical time for completing setting promotes.
By the above process, the present invention carries out experimental data such as 1 institute of table of the unsteady solution of large-scale parallel dual-time scale
Show.
Table 1, the present invention and conventional method carry out the Experimental comparison of the unsteady solution of large-scale parallel dual-time scale:
By table 1 it is found that the robustness of this technology is compared with the traditional method, in calculating process, maximum allowable CFL condition number
A magnitude or more is generally promoted, the robustness of this technology is demonstrated；The computational efficiency of this technology is compared with the traditional method, prediction
Efficiency generally promotes magnitude or more, demonstrates the forecasting efficiency of this technology.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.
Claims (8)
1. a kind of efficient implicit time propulsion method based on high accurate scheme and local airflow variable, which is characterized in that including
Following steps:
Step 1, it gives calculating grid and subdivision obtains grid block, the control unit for calculating grid block using interior loop iteration is minimum
Right-hand vector；
Step 2, the control unit minimum right-hand vector based on grid block corrects inner iteration virtual time step-length；
Step 3, by revised inner iteration virtual time step-length substitute into loop iteration solve governing equation time term from
Equation is dissipated, until completing the propulsion of a real time step；
Step 4, step 1~3 are repeated, until the physical time for completing setting promotes.
2. the efficient implicit time propulsion method according to claim 1 based on high accurate scheme and local airflow variable,
It is characterized in that, the calculation formula of the control unit minimum right-hand vector amendment inner iteration virtual time step-length based on grid block is such as
Under:
Δτ*=max [(RB-min/R0)1.0/power,threshold]*Δτ；
In formula, Δ τ*It is revised inner iteration virtual time step-length；Δ τ indicates the inner iteration virtual time step-length before amendment；
RB-minIt is the control unit minimum right-hand vector of grid block；R0It is the control unit right-hand vector when ground grid；Power is repairing for setting
Positive exponent；Threshold is the correction threshold of setting.
3. the efficient implicit time propulsion method according to claim 2 based on high accurate scheme and local airflow variable,
It is characterized in that, the modified index power set is 0.5~6.0.
4. the efficient implicit time propulsion method according to claim 3 based on high accurate scheme and local airflow variable,
It is characterized in that, for the relatively large grid block of control unit right-hand vector difference, the value phase of the modified index power of setting
To smaller.
5. the efficient implicit time propulsion method according to claim 2 based on high accurate scheme and local airflow variable,
It is characterized in that, the correction threshold threshold set is 0.01~1.0.
6. the efficient implicit time propulsion method according to claim 5 based on high accurate scheme and local airflow variable,
For the relatively large grid block of control unit right-hand vector difference, the value of the correction threshold threshold of setting is relatively small.
7. the efficient implicit time propulsion method according to claim 1 based on high accurate scheme and local airflow variable,
The establishment process of the discrete equation of the time term of the governing equation are as follows:
(1) governing equation is discrete using high order spatial format, half discrete form for obtaining governing equation is as follows:
In formula, Q is conservation variable, H and HvRespectively without viscous and sticky flux；All remainders for remembering governing equation are R (Q).
(2) virtual time inverse is introduced, difference is discrete after carrying out 3 points of second order accuracy to the time term of governing equation, obtain described
The discrete equation of the time term of governing equation is as follows:
In formula, p indicates that physics time step, Δ t indicate that real time step, m indicate that virtual time promotes step number, and Δ τ indicates empty
Pseudotime step-length.
8. the efficient implicit time propulsion method according to claim 7 based on high accurate scheme and local airflow variable,
It is described that revised inner iteration virtual time step-length is substituted into the discrete equation that interior loop iteration solves the time term of governing equation
Process are as follows:
(1) flux and viscosity are glued using the nothing of the discrete equation left end for the time term for calculating governing equation with cell centered scheme windward
Flux obtains the discrete equation expansion of the time term of governing equation:
In formula, Av,Bv,CvIndicate the coefficient matrix obtained by sticky flux derivation, δ+And δ-It is operator windward；
(2) D is enabled,It is diagonal matrix, lower triangular matrix and upper triangular matrix respectively, then has:
(3) it enablesThen the discrete equation expansion of the time term of governing equation is similar to following equation:
LD-1UδQm=R (Qm)；
(4) it takes
Then have
In formula,Expression A, the spectral radius of B, C, | Av,j|,|Bv,k|,|Cv,l| indicate these three viscous matrixs
A norm；
(5) by LD-1UδQm=R (Qm) resolve into three formula forms:
(6) first in step (5) and third operator are solved with chasing method, the solution of second operator only need to be marked simply
Amount is inverted, until two magnitudes drop in the discrete equation mean residual of the time term of governing equation, completes a real time step
Propulsion.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116070552A (en) * | 2023-03-15 | 2023-05-05 | 中国空气动力研究与发展中心计算空气动力研究所 | Calculation method and device for non-sticky flux, terminal equipment and storage medium |
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|---|---|---|---|---|
| CN104636566A (en) * | 2015-03-13 | 2015-05-20 | 中国矿业大学 | Dynamic mesh numerical solution method based on modified fluid motion equation |
| CN107766288A (en) * | 2017-10-19 | 2018-03-06 | 中国空气动力研究与发展中心计算空气动力研究所 | For the efficient implicit time propulsion method of robust of high accurate scheme |
| CN107977542A (en) * | 2018-01-25 | 2018-05-01 | 鲁东大学 | A kind of wave and the computational methods of arc plate-type breakwater interaction |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104636566A (en) * | 2015-03-13 | 2015-05-20 | 中国矿业大学 | Dynamic mesh numerical solution method based on modified fluid motion equation |
| CN107766288A (en) * | 2017-10-19 | 2018-03-06 | 中国空气动力研究与发展中心计算空气动力研究所 | For the efficient implicit time propulsion method of robust of high accurate scheme |
| CN107977542A (en) * | 2018-01-25 | 2018-05-01 | 鲁东大学 | A kind of wave and the computational methods of arc plate-type breakwater interaction |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116070552A (en) * | 2023-03-15 | 2023-05-05 | 中国空气动力研究与发展中心计算空气动力研究所 | Calculation method and device for non-sticky flux, terminal equipment and storage medium |
| CN116070552B (en) * | 2023-03-15 | 2023-06-27 | 中国空气动力研究与发展中心计算空气动力研究所 | Calculation method and device for non-sticky flux, terminal equipment and storage medium |
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Application publication date: 20190927 |