CN104331599A - Unstructured grid nesting wave numerical simulation method - Google Patents

Abstract

The invention discloses an unstructured grid nesting wave numerical simulation method, which includes the following main steps: an unstructured grid is adopted to create a mathematical model of waves in a large area; an unstructured grid is adopted to create a mathematical model of waves in a shallow-water engineering sea area; according to computational domains of different sizes, the numerical simulation of the waves is carried out. The unstructured grid nesting wave numerical simulation method achieves the following advantages: on the basis of bringing the unstructured grid wave mathematical models into full play, by applying the grid nesting technology, the unstructured grid nesting wave numerical simulation method greatly reduces the number of the grids in the computational domains, and increases the speed of computation; by applying the grid nesting technology, the unstructured grid nesting wave numerical simulation method can deploy finer computational grids in order to adapt to complex terrains and irregular coast boundaries, so that the accuracy of computed results can be increased.

Description

A kind of nested Numerical modeling of waves method of unstructured grid

Technical field

The present invention relates to a kind of nested Numerical modeling of waves method of unstructured grid, belong to wave field numerical simulation and forecasting technique field.

Background technology

In recent years, along with China's harbor approach engineering, man-made island, artificial sandy beach, enclose and cultivate, the construction of the coastal engineering such as wind-powered electricity generation, the numerical simulation of engineering marine site wave and prediction are had higher requirement.Set up unstructured grid river mouth, seashore and offshore engineering marine site wave mathematical model, accurate forecast engineering marine site element of wave, for optimizing engineering design scheme, cost saving, raising engineering safety, has important practical significance.

In order to simulate the process of wave propagation of river mouth, seashore and offshore waters more exactly, usually adopting the method for Grid Nesting, setting up the wave mathematical model of large and small scope.At present, conventional is both at home and abroad the Nesting Technique of structured grid, but because these waters landform are very complicated, water front is tortuous changeable, the impact of audient's multiple-project again simultaneously, fails the propagation of more accurate simulation wave.

Along with the development of Numerical modeling of waves technology, for structured grid, unstructured grid has more advantage, obtain extensive application, so far, although domestic and international application unstructured grid analogue technique achieves many successful stories, due to river mouth, seashore and the complicacy of offshore waters wave simulation and the accuracy requirement of Geng Gao, analog result needs to be improved further.

Summary of the invention

For solving the deficiencies in the prior art, the object of the present invention is to provide a kind of nested Numerical modeling of waves method of unstructured grid, set up the nested wave mathematical model in large and small region considering tidal level variable effect, to predicting the process of wave propagation of complicated landform, tortuous border and Effects on Engineering exactly.

In order to realize above-mentioned target, the present invention adopts following technical scheme:

A kind of nested Numerical modeling of waves method of unstructured grid, is characterized in that, comprise the steps:

1) set up the unstructured grid wave mathematical model of large regions, its governing equation is:

$\frac{\∂}{\∂t}N+\frac{\∂}{\∂x}{C}_{x}N+\frac{\∂}{\∂y}{C}_{y}N+\frac{\∂}{\∂\mathrm{\σ}}{C}_{\mathrm{\σ}}N+\frac{\∂}{\∂\mathrm{\θ}}{C}_{\mathrm{\θ}}N=\frac{S}{\mathrm{\σ}}---\left(1\right)$

Above formula left side Section 1 is wave action N rate over time, and N=N (σ, θ)=E (σ, θ)/σ, E (σ, θ) is energy spectral density, and σ is wave frequencies, and θ is wave direction;

Above formula left side Section 2 and Section 3 represent the propagation of N (σ, θ) on x, y direction, space respectively;

Above formula left side Section 4 represents N (σ, θ) in σ space because flow field and the change caused by the depth of water;

Above formula left side Section 5 represents the propagation of N (σ, θ) in θ space, that is the depth of water and the refraction caused by flow field;

S on the right of equation represents the source sink term represented with spectral density, comprise wind energy input, between ripple and ripple nonlinear interaction and due to end friction, whitecap, the degree of depth induction fragmentation caused by energy loss;

Described C _x, C _y, C _σ, C _θrepresent the wave celerity in x, y, σ, θ space respectively; Wherein, C _x, C _y, C _σ, C _θbe respectively:

$C_x=\frac{\mathrm{dx}}{\mathrm{dt}}=\frac{1}{2}[1+\frac{2\mathrm{kd}}{\sinh \left(2\mathrm{kd}\right)}]\frac{{\mathrm{\σk}}_x}{k^2}+U_x---\left(2\right)$

$C_y=\frac{\mathrm{dy}}{\mathrm{dt}}=\frac{1}{2}[1+\frac{2\mathrm{kd}}{\sinh \left(2\mathrm{kd}\right)}]\frac{{\mathrm{\σk}}_y}{k^2}+U_y---\left(3\right)$

$C_{\mathrm{\σ}}=\frac{\mathrm{d\σ}}{\mathrm{dt}}=\frac{\∂\mathrm{\σ}}{\∂d}[\frac{\∂d}{\∂t}+\stackrel{\→}{U}\·\▿d]-C_g\stackrel{\→}{k}\·\frac{\∂\stackrel{\→}{U}}{\∂s}---\left(4\right)$

$C_{\mathrm{\θ}}=\frac{\mathrm{d\θ}}{\mathrm{dt}}=\frac{1}{k}[\frac{\∂\mathrm{\σ}}{\∂d}\frac{\∂d}{\∂m}+\stackrel{\→}{k}\·\frac{\stackrel{\→}{U}}{\∂m}]---\left(5\right)$

Wherein for wave number, k _x,k _ybe respectively the component in x, u space, k is wave number, and d is the depth of water, for flow velocity, U _x,u _ybe respectively the component in x, y space, s is along θ director space coordinate, and m is the coordinate perpendicular to s, relative frequency ω is the natural frequency of wave; Operator be defined as $\frac{d}{\mathrm{dt}}=\frac{\∂}{\∂t}+\stackrel{\→}{C}\·{\▿}_{x,y};$ for velocity of wave; T is the time.

2) engineering marine site, the shallow sea wave mathematical model that unstructured grid is nested is set up; The completely nested frequency spectrum provided according to described large regions unstructured grid wave mathematical model and directional spectrum boundary condition (comprising the key elements such as the coordinate of computational fields boundary node that will be nested, frequency, direction, power spectrum or variable density), then apply described step 1) in governing equation and relevant subsidiary equation, set up engineering marine site, shallow sea wave mathematical model, carry out the wave simulation of engineering marine site;

3) the nested wave mathematical model of described unstructured grid is solved.

The nested Numerical modeling of waves method of aforesaid a kind of unstructured grid, is characterized in that, described step 1) in, the expression formula of source function item S is:

S＝S _wind+S _nl+S _bottom+S _white+S _breaking(6)；

S _windrepresent the effect of wind to wave; S _nlrepresent the interaction between nonlinear wave-Bo; S _bottomrepresent the energy loss caused by end friction; S _whiterepresent the energy loss caused by whitecap; S _breakingrepresent the energy loss of degree of depth induction caused by fragmentation.

The nested Numerical modeling of waves method of aforesaid a kind of unstructured grid, is characterized in that, described S _wind, i.e. S _wind(σ, θ), represents the effect of wind to wave, can be expressed as linear increase part and exponential increase part, that is: S _wind(σ, θ)=A+BE (σ, θ), wherein A and B depends on the size and Orientation of wave frequency, direction and wind.

The nested Numerical modeling of waves method of aforesaid a kind of unstructured grid, is characterized in that, described S _nlrepresent Nonjinear Wava, wave is grown up obtain energy from wind after, and its energy is reallocated again between different frequency; Three-phase wave-wave interaction obtains according to the scheme of E1deberky (1996) and utilizes the method for LTA (Lumped Triad Approximation) to solve; The scheme that the calculating of four phase wave-wave interactions adopts Hasselmann (1985) to propose, and adopt DIA (Discrete interaction approximation) method

The nested Numerical modeling of waves method of aforesaid a kind of unstructured grid, is characterized in that, described S _bottomrepresent the energy loss caused by end friction, expression formula is:

$S_{\mathrm{bottom}}(\mathrm{\σ},\mathrm{\θ})=-C_{\mathrm{bottom}}\frac{{\mathrm{\σ}}^2}{g^2{\sinh }^2\left(\mathrm{kd}\right)}E(\mathrm{\σ},\mathrm{\θ})---\left(7\right)$

D is the depth of water, and σ, k and θ represent frequency, wave number and wave direction respectively, and g is acceleration of gravity, C _bottomit is bottom-friction factor.

The nested Numerical modeling of waves method of aforesaid a kind of unstructured grid, is characterized in that, described S _whiterepresent the energy loss caused by whitecap, expression formula is:

$S_{\mathrm{white}}(\mathrm{\σ},\mathrm{\θ})=-\mathrm{\Γ}\widetilde{\mathrm{\σ}}\frac{k}{\tilde{k}}E(\mathrm{\σ},d)---\left(8\right)$

In formula, d represents the depth of water, and Γ is wave steepness coefficient, and E (σ, d) is wave energy, and k is wave number, represent average frequency, represent average wave number.

The nested Numerical modeling of waves method of aforesaid a kind of unstructured grid, is characterized in that, described S _breakingrepresent the energy loss of degree of depth induction caused by fragmentation, expression formula is:

$S_{\mathrm{breaking}}(\mathrm{\σ},\mathrm{\θ})=-D_{\mathrm{tot}}\frac{E(\mathrm{\σ},\mathrm{\θ})}{E_{\mathrm{tot}}}---\left(9\right)$

Wherein, E _totfor total wave energy, D _totfor ripple fragmentation causes the mean dissipation rate of energy in unit area, its expression formula is:

$D_{\mathrm{tot}}=-\frac{1}{4}{\mathrm{\α}}_{\mathrm{BJ}}{Q}_b\left(\frac{\widetilde{\mathrm{\σ}}}{2\mathrm{\π}}\right)H_m^2---\left(10\right)$

Wherein, α in SWAN model _bJ=1, for average frequency, Q _bdetermined by the ripple of fragmentation:

$\frac{1-Q_b}{\ln Q_b}=-8\frac{E_{\mathrm{tot}}}{H_m^2}---\left(11\right)$

H _mfor given depth wave fails the broken maximum wave height that can support to occur, by H _m=γ d determines, wherein d is the depth of water, and γ is breakage parameter, is taken as constant, and default value is 0.73.

The nested Numerical modeling of waves method of aforesaid a kind of unstructured grid, it is characterized in that, described step 3) in, with third generation wave model SWAN for instrument, integrating step 1) in formula (1) in fundamental equation and correlation formula, and applying step 2) in result, adopt fully implicit solution finite difference scheme to solve the nested wave mathematical model of described unstructured grid with an iteration four scanning techniques.

The beneficial effect that the present invention reaches: on the basis giving full play to unstructured grid wave mathematical model, by application Grid Nesting Technique, substantially reduce the quantity of grid in computational fields, reduce the difference of maximum mesh and minimum grid, improve computing velocity.By application Grid Nesting Technique, meticulousr computing grid can be arranged, adapt to complicated landform, tortuous water front border, improve the accuracy of result of calculation.

Accompanying drawing explanation

figure1 is SWAN model computer capacity on a large scale;

figure2 is SWAN model meshes on a large scale;

figure3 is During Typhoon (No. 8615) zoning significant wave height distribution on a large scale figure;

figure4 is SWAN Project Areas model computer capacity;

figure5 is SWAN Project Areas model computing grid;

figure6 is the distribution of During Typhoon (No. 8615) Engineering Zone significant wave height figure;

figure7 is frequency spectrum and the signal of directional spectrum boundary condition figure;

figure8 illustrate for wave calculates reference mark figure;

figure9 is 2 years chance+strong breeze extensive area NE direction H13% Wave Height Distribution figure;

figure10 is 2 years NE direction, chance+strong breeze Engineering Zone H13% Wave Height Distribution figure.

Embodiment

Below in conjunction with attached figurethe invention will be further described.Following examples only for technical scheme of the present invention is clearly described, and can not limit the scope of the invention with this.

A kind of nested Numerical modeling of waves method of unstructured grid, in conjunction with some typical methods in the past, comprises the steps:

1) set up the unstructured grid wave mathematical model of large regions, its governing equation is:

$\frac{\∂}{\∂t}N+\frac{\∂}{\∂x}{C}_{x}N+\frac{\∂}{\∂y}{C}_{y}N+\frac{\∂}{\∂\mathrm{\σ}}{C}_{\mathrm{\σ}}N+\frac{\∂}{\∂\mathrm{\θ}}{C}_{\mathrm{\θ}}N=\frac{S}{\mathrm{\σ}}---\left(1\right)$

Above formula left side Section 1 is wave action N rate over time, and N=N (σ, θ)=E (σ, θ)/σ, E (σ, θ) is energy spectral density, and σ is wave frequencies, and θ is wave direction;

Above formula left side Section 2 and Section 3 represent the propagation of N (σ, θ) on x, y direction, space respectively;

Above formula left side Section 4 represents N (σ, θ) in σ space because flow field and the change caused by the depth of water;

Above formula left side Section 5 represents the propagation of N (σ, θ) in θ space, that is the depth of water and the refraction caused by flow field;

S on the right of equation represents the source sink term represented with spectral density, comprise wind energy input, between ripple and ripple nonlinear interaction and due to end friction, whitecap, the degree of depth induction fragmentation caused by energy loss;

C _x, C _y, C _σ, C _θrepresent the wave celerity in x, y, σ, θ space respectively; Wherein, C _x, C _y, C _σ, C _θbe respectively:

$C_x=\frac{\mathrm{dx}}{\mathrm{dt}}=\frac{1}{2}[1+\frac{2\mathrm{kd}}{\sinh \left(2\mathrm{kd}\right)}]\frac{{\mathrm{\σk}}_x}{k^2}+U_x---\left(2\right)$

$C_y=\frac{\mathrm{dy}}{\mathrm{dt}}=\frac{1}{2}[1+\frac{2\mathrm{kd}}{\sinh \left(2\mathrm{kd}\right)}]\frac{{\mathrm{\σk}}_y}{k^2}+U_y---\left(3\right)$

$C_{\mathrm{\σ}}=\frac{\mathrm{d\σ}}{\mathrm{dt}}=\frac{\∂\mathrm{\σ}}{\∂d}[\frac{\∂d}{\∂t}+\stackrel{\→}{U}\·\▿d]-C_g\stackrel{\→}{k}\·\frac{\∂\stackrel{\→}{U}}{\∂s}---\left(4\right)$

$C_{\mathrm{\θ}}=\frac{\mathrm{d\θ}}{\mathrm{dt}}=\frac{1}{k}[\frac{\∂\mathrm{\σ}}{\∂d}\frac{\∂d}{\∂m}+\stackrel{\→}{k}\·\frac{\stackrel{\→}{U}}{\∂m}]---\left(5\right)$

Wherein for wave number, k _x,k _ybe respectively the component in x, y space, k is wave number, and d is the depth of water, for flow velocity, U _x,u _ybe respectively the component in x, y space, s is along θ director space coordinate, and m is the coordinate perpendicular to s, relative frequency ω is the natural frequency of wave; Operator be defined as $\frac{d}{\mathrm{dt}}=\frac{\∂}{\∂t}+\stackrel{\→}{C}\·{\▿}_{x,y};$ for velocity of wave; T is the time.

The expression formula of source function item S is:

S＝S _wind+S _nl+S _bottom+S _white+S _breaking(6)；

S _windrepresent the effect of wind to wave; S _nlrepresent the interaction between nonlinear wave-Bo; S _bottomrepresent the energy loss caused by end friction; S _whiterepresent the energy loss caused by whitecap; S _breakingrepresent the energy loss of degree of depth induction caused by fragmentation.

S _wind, i.e. S _wind(σ, θ), represent the effect of wind to wave, the combining form of the parallel-flow instability stormy waves generative theory that " resonance " mechanism adopting Phillips (1957) to propose and Miles (1957) propose, linear increase part and exponential increase part, that is: S can be expressed as _wind(σ, θ)=A+BE (σ, θ), wherein A and B depends on the size and Orientation of wave frequency, direction and wind, and coefficient A, B choose the analog result directly affecting wave.

S _nlrepresent Nonjinear Wava, wave is grown up obtain energy from wind after, and its energy is reallocated again between different frequency.In deep water situation, four phase wave-wave interactions control the development of wave wave spectrum, and it from high-frequency transfer (HFT) to low frequency, makes peak frequently move to low frequency gradually part energy; In shallow water, three-phase wave-wave interaction plays a major role, by the energy of low frequency to high frequency conversion.In offshore shoal water zone, because submarine topography is complicated and changeable, therefore generally three ripple S must be considered _nl3(σ, θ) and four ripple S _nl4interaction between (σ, θ).

Three-phase wave-wave interaction obtains according to the scheme of E1deberky (1996) and utilizes the method for LTA (Lumped Triad Approximation) to solve:

$S_{\mathrm{nl}3}(\mathrm{\σ},\mathrm{\θ})=S_{\mathrm{nl}3}^{+}(\mathrm{\σ},\mathrm{\θ})+S_{\mathrm{nl}3}^{-}(\mathrm{\σ},\mathrm{\θ});$

$S_{\mathrm{nl}3}^{+}(\mathrm{\σ},\mathrm{\θ})\max \{0,{\mathrm{\α}}_{\mathrm{EB}}2{\mathrm{\πCC}}_g{J}^2|\sin \mathrm{\β}\left|\right[E^2(\frac{\mathrm{\σ}}{2},\mathrm{\θ})-2E(\frac{\mathrm{\σ}}{2},\mathrm{\θ})E(\mathrm{\σ},\mathrm{\θ})\left]\right\}$

$S_{\mathrm{nl}3}^{-}(\mathrm{\σ},\mathrm{\θ})=-{2S}_{\mathrm{nl}3}^{+}(\mathrm{\σ},\mathrm{\θ})$

$\mathrm{\β}=-\frac{2}{\mathrm{\π}}+\frac{2}{\mathrm{\π}}\tanh \left(\frac{0.2}{U_r}\right)$

The expression formula of interaction coefficient J is:

Wherein, as 10 > U _rjust calculate during > 0.1.

α _eBfor adjustable scale-up factor, H _sfor significant wave height, σ is wave frequencies, and θ is wave direction, and k is wave number, and d is the depth of water, and g is acceleration of gravity, and C is velocity of wave, C _gfor group velocity, E (σ, θ) is energy spectral density, T, be respectively average wave cycle and average wave frequencies.

The scheme that the calculating of four phase wave-wave interactions adopts Hasselmann (1985) to propose, and adopt DIA (Discrete Interaction Approximation) method:

Four wave frequencies are got:

σ ₁=σ ₂=σ, σ ₃=σ (1+ λ)=σ ⁺, σ ₄=σ (1-λ)=σ ^-, λ is constant, gets λ=0.25.

In DIA method, consider two group of four ripple, first group is second group is so source item S _nl4(σ, θ) can be expressed as:

$S_{\mathrm{nl}4}(\mathrm{\σ},\mathrm{\θ})=S_{\mathrm{nl}4}^{*}(\mathrm{\σ},\mathrm{\θ})+S_{\mathrm{nl}4}^{**}(\mathrm{\σ},\mathrm{\θ})$

Wherein, expression formula with direction of mirror image is consistent.

$\begin{array}{c}\left(\begin{array}{c}{\mathrm{\δS}}_{\mathrm{nl}4}^{*}(\mathrm{\σ},\mathrm{\θ})\\ {\mathrm{\δS}}_{\mathrm{nl}4}^{*}({\mathrm{\σ}}^{+},{\mathrm{\θ}}^{+})\\ {\mathrm{\δS}}_{\mathrm{nl}4}^{*}({\mathrm{\σ}}^{-},{\mathrm{\θ}}^{-})\end{array}\right)=\left(\begin{array}{c}2\\ -1\\ -1\end{array}\right)C_{\mathrm{nl}4}{\left(2\mathrm{\π}\right)}^2{g}^{-4}{\left(\frac{\mathrm{\σ}}{2\mathrm{\π}}\right)}^{11}\×\\ \left\{E^2(\mathrm{\σ},\mathrm{\θ})\right[\frac{E({\mathrm{\σ}}^{+},{\mathrm{\θ}}^{+})}{{(1+\mathrm{\λ})}^4}+\frac{E({\mathrm{\σ}}^{-},{\mathrm{\θ}}^{-})}{{(1-\mathrm{\λ})}^4}]-2\frac{E(\mathrm{\σ},\mathrm{\θ})E({\mathrm{\σ}}^{+},{\mathrm{\θ}}^{+})E({\mathrm{\σ}}^{-},{\mathrm{\θ}}^{-})}{{(1-{\mathrm{\λ}}^2)}^4}\}\end{array}$

In formula, C _nl4for constant, get 3 × 10 ⁷, energy spectral density E (σ ⁺, θ ⁺), E (σ ^-, θ ^-) obtained by bilinear interpolation according to around four values.

S _bottomrepresent the energy loss caused by end friction, expression formula is:

$S_{\mathrm{bottom}}(\mathrm{\σ},\mathrm{\θ})=-C_{\mathrm{bottom}}\frac{{\mathrm{\σ}}^2}{g^2{\sinh }^2\left(\mathrm{kd}\right)}E(\mathrm{\σ},\mathrm{\θ})---\left(7\right)$

D is the depth of water, and σ, k and θ represent frequency, wave number and wave direction respectively, and g is acceleration of gravity, and E (σ, θ) is energy spectral density, C _bottombe bottom-friction factor, Hasselmann et al. (1973) value in JONSWAP experiment is 0.038m ²s ^-3, Bouws and Komen (1983) gets 0.067m under shallow water Developed state ²s ^-3.

S _whiterepresent the energy loss caused by whitecap, sea is (particularly strong wind) under the continuous action of wind, and stormy waves constantly produces, grow up, and wherein a part is broken, ripple is broken directly forms ocean whitecap, and the foam stayed after whitecap decline wants the long period to wither away; Meanwhile, drip with the also have bubble in seawater and the foam in air of whitecap association.Whitecap plays an important role in air-sea exchange process.Choose the expression formula of WAMDIgroup (1988):

$S_{\mathrm{white}}(\mathrm{\σ},\mathrm{\θ})=-\mathrm{\Γ}\widetilde{\mathrm{\σ}}\frac{k}{\tilde{k}}E(\mathrm{\σ},d)---\left(8\right)$

In formula, d represents the depth of water, and Γ is wave steepness coefficient, depends on equal square wave steep, adopts the formula of G ü nther et al. (1992).

S _breakingrepresent the energy loss of degree of depth induction caused by fragmentation, expression formula is:

$S_{\mathrm{breaking}}(\mathrm{\σ},\mathrm{\θ})=-D_{\mathrm{tot}}\frac{E(\mathrm{\σ},\mathrm{\θ})}{E_{\mathrm{tot}}}---\left(9\right)$

Wherein, Etot is total wave energy, and Dtot is the mean dissipation rate that ripple fragmentation causes energy in unit area, and its expression formula is:

$D_{\mathrm{tot}}=-\frac{1}{4}{\mathrm{\α}}_{\mathrm{BJ}}{Q}_b\left(\frac{\widetilde{\mathrm{\σ}}}{2\mathrm{\π}}\right)H_m^2---\left(10\right)$

Wherein, α in SWAN model _bJ=1, for average frequency, Q _bdetermined by the ripple of fragmentation:

$\frac{1-Q_b}{\ln Q_b}=-8\frac{E_{\mathrm{tot}}}{H_m^2}---\left(11\right)$

H _mfor given depth wave fails the broken maximum wave height that can support to occur, by H _m=γ d determines, wherein d is the depth of water, and γ is breakage parameter, is taken as constant, and default value is 0.73.

2) engineering marine site, the shallow sea wave mathematical model that unstructured grid is nested is set up.The completely nested frequency spectrum of engineering marine site wave mathematical model and directional spectrum boundary condition (comprising the key elements such as the coordinate of computational fields boundary node that will be nested, frequency, direction, power spectrum or variable density) is supplied to according to large regions unstructured grid wave mathematical model, then applying step 1) in governing equation and relevant subsidiary equation, set up engineering marine site, shallow sea wave mathematical model, carry out engineering marine site wave numerical evaluation.

3) the nested wave mathematical model of unstructured grid is solved.

With third generation wave model SWAN for instrument, integrating step 1) in formula (1) in fundamental equation and correlation formula, and applying step 2) in result, adopt fully implicit solution finite difference scheme to solve the nested wave mathematical model of described unstructured grid with an iteration four scanning techniques.

In conjunction with the embodiments: carry out analytic explanation for the clear out a harbour navigation safety problem midchannel of Haihe River, navigation channel through transport and the wave propagation situation in waters, wharf apron of Sheyang Harbor.

(1) large regions unstructured grid wave mathematical model is set up

According to " PORT OF YANCHENG general plan ", Sheyang Harbor divides into operation area, inland river and operation area, river mouth, wherein, the North, shining sun river mouth of operation area, river mouth plans to give priority to district at no distant date, based on coal, loose groceries, container, fluid chemical and petroleum product transport.

To clear out a harbour waterway engineering requirement according to Sheyang Harbor, Sheyang Harbor will utilize yellow sand port directly to realize Haihe River through transport, and inland navigation craft directly sails shining sun river mouth sea port dock into, and " seamless " that realize Haihe River through transport is connected.

Therefore, the feasibility of shining sun river mouth waterfront area is directly sailed in order to fully prove inland navigation craft, there is provided scientific basis to the clear out a harbour design of waterway engineering and decision-making section of Sheyang Harbor, carry out Sheyang Harbor and to clear out a harbour the navigation safety problem midchannel of Haihe River, navigation channel through transport and the wave propagation numerical simulation in waters, wharf apron.

In order to the wave propagation in accurate simulation Haihe River through transport midchannel and waters, wharf apron, first applying step 1) in governing equation and relevant subsidiary equation, establish wave model SWAN on a large scale, corresponding zoning underwater topography and grid as figure1 He figureshown in 2, can stage-17 meters of sea-bottom contour place elements of wave according to work, calculate the element of wave at-12 meters of depth of water places, and carried out the wave field simplation verification of No. 8615 During Typhoon Sheyang Harbor surrounding waters, significant wave height distribution as figureshown in 3, by calculating ,-12 meters of sea-bottom contour place H4% wave height are 5.24 meters, with ocean one the wave height 5.3 meters that draws according to field data analysis comparatively close, for Engineering Zone model provides boundary condition.

(2) engineering marine site, the shallow sea wave mathematical model that unstructured grid is nested is set up

According to the boundary condition (comprising the key elements such as the coordinate of computational fields boundary node that will be nested, frequency, direction, power spectrum or variable density) that wave model on a large scale provides, applying step 2) establish Project Areas wave model, this north and south, region is at a distance of about 17 kilometers thingbe about 34 kilometers, in order to accurate simulation engineering and topography variation, on the impact of wave propagation, have carried out local refinement to Engineering Zone grid more, have 48094 nodes, triangular element 93883, the minimum length of side of grid is 10m, its zoning underwater topography and grid as figure4 Hes figureshown in 5, if press this computational fields of mesh generation of 10m × 10m, will have 5780000 rectangular nodes, be more than 60 times of triangle gridding, visible method of the present invention can save computing time greatly, increases the benefit.Surrounding waters, No. 8615 During Typhoon Sheyang Harbor river mouths and clear out a harbour waters, navigation channel significant wave height distribution as figureshown in 6, be mainly used in research breakwater engineering and clear out a harbour the impact of waterway engineering on surrounding waters element of wave, and providing element of wave for ship seakeeping, alongside calculating and operation simulation.

(3) realization of the nested wave mathematical model of unstructured grid

The completely nested frequency spectrum provided according to large regions wave model and directional spectrum boundary condition (comprising the key elements such as the coordinate of computational fields boundary node that will be nested, frequency, direction, power spectrum or variable density), its boundary condition is illustrated figureas figureshown in 7, the engineering marine site wave simulation for fine grid blocks (minimum grid length of side 10m) more calculates.

(4) impact on surrounding waters wave field such as unstructured grid nested wave mathematical model research coastal engineering, port boat engineering is applied.

The nested wave mathematical model of the unstructured grid set up above application, according to step 3) solve the nested wave mathematical model of unstructured grid, research breakwater engineering and the impact of waterway engineering on Sheyang Harbor surrounding waters wave field of clearing out a harbour, calculate the element of wave of each calculation level when Haihe River terminal basin under various working condition and boats and ships navigate by water from turnover Haihe River, yellow sand port terminal, for ship maneuvering simulator carries out clearing out a harbour the wave condition that Haihe River, navigation channel through transport navigation condition analogue simulation provides necessary, carry out NE, ENE both direction is 50 years one chances under design high-water condition, 25 years one chances, the Wave parameters of meeting three reoccurrence periods for 2 years one calculates, obtain H13% wave height, wherein within 25 years one, meeting and within 50 years one, meeting wave calculation of wind speed adopts strong gale to represent wind speed, within 2 years one, meeting wave adopts strong breeze and moderate gale to represent wind speed as calculation of wind speed respectively.Wave calculate reference mark as figureshown in 8.

Wherein, distribute to significant wave height with Engineering Zone NE on a large scale accordingly figureas figure9, figureshown in 10.

Wherein, design high-water+2 years meets each calculating reference mark significant wave height statistics as table 1shown in.

Under within 2 years one, meeting wave situations, Haihe River terminal basin and neighbouring each point (P1 ~ P7) wave height are reduced gradually by P1 to P7, under strong breeze condition, H13% wave height maximal value is 0.618m, and under moderate gale condition, H13% wave height maximal value is 0.66m, all occur in NE direction; And respectively calculate reference mark (Q1 ~ Q20) all directions H13% wave height under strong breeze and moderate gale condition from yellow sand port to Haihe River terminal section and be substantially all less than 0.4m.

The beneficial effect that the present invention reaches: on the basis giving full play to unstructured grid wave mathematical model, by application Grid Nesting Technique, substantially reduce the quantity of grid in computational fields, reduce the difference of maximum mesh and minimum grid, improve computing velocity.By application Grid Nesting Technique, meticulousr computing grid can be arranged, adapt to complicated landform, tortuous water front border, improve the accuracy of result of calculation.The unstructured grid nested wave mathematical model computer capacity that the present invention sets up covers from deep water sea area to river mouth, the whole engineering waters in river course, utilize actual measurement Wave Data, carry out the checking of nested wave mathematical model, result of calculation is reasonable, and apply this model, to clear out a harbour for Sheyang Harbor the navigation safety problem of Haihe River, navigation channel through transport, carried out the Numerical modeling of waves in navigation channel and waters, wharf apron, analyzed the distribution characteristics of wave on this basis.

table 1design high-water+2 years one meets each calculating reference mark significant wave height statistics

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the prerequisite not departing from the technology of the present invention principle; can also make some improvement and distortion, these improve and distortion also should be considered as protection scope of the present invention.

Claims (8)

1. the nested Numerical modeling of waves method of unstructured grid, is characterized in that, comprise the steps:

1) set up the unstructured grid wave mathematical model of large regions, its governing equation is:

$\frac{\∂}{\∂t}N+\frac{\∂}{\∂x}{C}_{x}N+\frac{\∂}{\∂y}{C}_{y}N+\frac{\∂}{\∂\mathrm{\σ}}{C}_{\mathrm{\σ}}N+\frac{\∂}{\∂\mathrm{\θ}}{C}_{\mathrm{\θ}}N=\frac{s}{\mathrm{\σ}}---\left(1\right)$

Above formula left side Section 1 is wave action N rate over time, and N=N (σ, θ)=E (σ, θ)/σ, E (σ, θ) is energy spectral density, and σ is wave frequencies, and θ is wave direction;

Above formula left side Section 2 and Section 3 represent the propagation of N (σ, θ) on x, y direction, space respectively;

Above formula left side Section 4 represents N (σ, θ) in σ space because flow field and the change caused by the depth of water;

Above formula left side Section 5 represents the propagation of N (σ, θ) in θ space, that is the depth of water and the refraction caused by flow field;

S on the right of equation represents the source sink term represented with spectral density, comprise wind energy input, between ripple and ripple nonlinear interaction and due to end friction, whitecap, the degree of depth induction fragmentation caused by energy loss;

Described C _x, C _y, C _σ, C _θrepresent the wave celerity in x, y, σ, θ space respectively; Wherein, C _x, C _y, C _σ, C _θbe respectively:

$C_x=\frac{\mathrm{dx}}{\mathrm{dt}}=\frac{1}{2}[1+\frac{2\mathrm{kd}}{\sinh \left(\mathrm{skd}\right)}]\frac{\mathrm{\σ}{k}_x}{k^2}+U_x---\left(2\right)$

$C_y=\frac{\mathrm{dy}}{\mathrm{dt}}=\frac{1}{2}[1+\frac{2\mathrm{kd}}{\sinh \left(2\mathrm{kd}\right)}]\frac{\mathrm{\σ}{k}_y}{k^2}+U_y---\left(3\right)$

$C_{\mathrm{\σ}}=\frac{\mathrm{d\σ}}{\mathrm{dt}}=\frac{\∂\mathrm{\σ}}{\∂d}[\frac{\∂d}{\∂t}+\stackrel{\→}{U}\·\▿d]-C_g\stackrel{\→}{k}\·\frac{\∂\stackrel{\→}{U}}{\∂s}---\left(4\right)$

$C_{\mathrm{\θ}}=\frac{\mathrm{d\θ}}{\mathrm{dt}}=\frac{1}{k}[\frac{\∂\mathrm{\σ}}{\∂d}\frac{\∂d}{\∂m}+\stackrel{\→}{k}\·\frac{\stackrel{\→}{U}}{\∂m}]---\left(5\right)$

Wherein, for wave number, k _x, k _ybe respectively the component in x, y space, k is wave number, and d is the depth of water, for flow velocity, U _x, u _ybe respectively 2 components in x, y space, s is along θ director space coordinate, and m is the coordinate perpendicular to s, relative frequency ω is the natural frequency of wave; Operator be defined as for velocity of wave; T is the time.

2) engineering marine site, the shallow sea wave mathematical model that unstructured grid is nested is set up; The completely nested frequency spectrum of engineering marine site, described shallow sea wave mathematical model and directional spectrum boundary condition (comprising the key elements such as the coordinate of computational fields boundary node that will be nested, frequency, direction, power spectrum or variable density) is supplied to according to described large regions unstructured grid wave mathematical model, then apply described step 1) in governing equation and relevant subsidiary equation, set up engineering marine site, shallow sea wave mathematical model, carry out engineering marine site wave numerical evaluation.

3) the nested wave mathematical model of described unstructured grid is solved.

2. the nested Numerical modeling of waves method of a kind of unstructured grid according to claim 1, is characterized in that, described step 1) in, the expression formula of source function item S is:

S＝S _wind+S _nl+S _bottom+S _white+S _breaking(6)；

S _windrepresent the effect of wind to wave; S _nlrepresent the interaction between nonlinear wave-Bo; S _bottomrepresent the energy loss caused by end friction; S _whiterepresent the energy loss caused by whitecap; S _breakingrepresent the energy loss of degree of depth induction caused by fragmentation.

3. the nested Numerical modeling of waves method of a kind of unstructured grid according to claim 2, is characterized in that, described S _wind, i.e. S _wind(σ, θ), represents the effect of wind to wave, is expressed as linear increase part and exponential increase part, that is: S _wind(σ, θ)=A+BE (σ, θ), wherein with the size and Orientation depending on wave frequency, direction and wind, E (σ, θ) is energy spectral density.

4. the nested Numerical modeling of waves method of a kind of unstructured grid according to claim 2, is characterized in that, described S _nlrepresent Nonjinear Wava, wave is grown up obtain energy from wind after, and its energy is reallocated again between different frequency; Describedly comprise three-phase wave-wave interaction S _nl3with four phase wave-wave interaction S _nl4.

5. the nested Numerical modeling of waves method of a kind of unstructured grid according to claim 2, is characterized in that, described S _bottomrepresent the energy loss caused by end friction, expression formula is:

$S_{\mathrm{bottom}}(\mathrm{\σ},\mathrm{\θ})=-C_{\mathrm{bottom}}\frac{{\mathrm{\σ}}^2}{g^2{\sinh }^2\left(\mathrm{kd}\right)}E(\mathrm{\σ},\mathrm{\θ})---\left(7\right)$

Wherein, d is the depth of water, and σ, k and θ represent frequency, wave number and wave direction respectively, C _bottombe bottom-friction factor, E (σ, θ) is energy spectral density.

6. the nested Numerical modeling of waves method of a kind of unstructured grid according to claim 2, is characterized in that, described S _whiterepresent the energy loss caused by whitecap, expression formula is:

$S_{\mathrm{white}}(\mathrm{\σ},\mathrm{\θ})=-\mathrm{\Γ}\widetilde{\mathrm{\σ}}\frac{k}{\tilde{k}}E(\mathrm{\σ},d)---\left(8\right)$

In formula, d represents the depth of water, and Γ is wave steepness coefficient, represent average frequency, represent average wave number.

7. the nested Numerical modeling of waves method of a kind of unstructured grid according to claim 2, is characterized in that, described step 1) in,

Described S _breakingrepresent the energy loss of degree of depth induction caused by fragmentation, expression formula is:

$S_{\mathrm{breaking}}(\mathrm{\σ},\mathrm{\θ})=-D_{\mathrm{tot}}\frac{E(\mathrm{\σ},\mathrm{\θ})}{E_{\mathrm{tot}}}---\left(9\right)$

Wherein, E _totfor total wave energy, D _totfor ripple fragmentation causes the mean dissipation rate of energy in unit area, its expression formula is:

$D_{\mathrm{tot}}=-\frac{1}{4}{\mathrm{\α}}_{\mathrm{BJ}}{Q}_b\left(\frac{\widetilde{\mathrm{\σ}}}{2\mathrm{\π}}\right)H_m^2---\left(10\right)$

Wherein, α in SWAN model _bJ=1, for average frequency, Q _bdetermined by the ripple of fragmentation:

$\frac{1-Q_b}{\ln Q_b}=-8\frac{E_{\mathrm{tot}}}{H_m^2}---\left(11\right)$

H _mfor given depth wave fails the broken maximum wave height that can support to occur, by H _m=γ d determines, wherein d is the depth of water, and γ is breakage parameter.

8. the nested Numerical modeling of waves method of a kind of unstructured grid according to claim 1, it is characterized in that, described step 3) in, with third generation wave model SWAN for instrument, integrating step 1) in governing equation (1) and relevant side formula, and applying step 2) in the nesting method of unstructured grid wave model, adopt fully implicit solution finite difference scheme to solve the nested wave mathematical model of described unstructured grid with an iteration four scanning techniques.