CN111523280B - Water flow simulation method based on space coupling integrated numerical model - Google Patents

Water flow simulation method based on space coupling integrated numerical model Download PDF

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CN111523280B
CN111523280B CN202010326471.7A CN202010326471A CN111523280B CN 111523280 B CN111523280 B CN 111523280B CN 202010326471 A CN202010326471 A CN 202010326471A CN 111523280 B CN111523280 B CN 111523280B
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张景新
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Abstract

A water flow simulation method based on a space coupling integrated numerical model is characterized in that a numerical model of water wave dynamics is established based on a finite volume method of a non-structural computational grid with a highly-fitted complex boundary; then, dividing the integral calculation domain into a non-dispersive water wave execution region and a dispersive water wave execution region which respectively and independently operate by the spatial region division, wherein different calculation models are adopted in different regions; the integration simulation of the dispersive and non-dispersive water wave models is realized among the areas, namely the area connection through constructing an exchange function; and finally establishing a coupled water wave numerical model for water flow simulation. The invention integrates and simulates the dispersion and non-dispersion numerical models in a unified way by the way of space computation domain subdivision combination. The discrete numerical formats of the control equations are unified, the dispersion mode locally operates, the data exchange is realized by interpolation of the region interfaces by taking the theoretical flow velocity profile as a basic template, and the organic combination of the simulation precision and the calculation efficiency is realized. The invention gives full play to the high efficiency of the non-dispersive water wave model simulation and the high precision of the dispersive water wave model simulation, and expands the application range of the two models by considering the advantages of the two models.

Description

Water flow simulation method based on space coupling integrated numerical model
Technical Field
The invention relates to a numerical simulation technology in the field of hydrodynamics, in particular to a water flow simulation method of a space coupling integrated numerical model based on a dispersion and non-dispersion water wave model.
Background
The non-dispersive shallow water wave model is widely applied to the research of water flow dynamics and the preliminary research of related engineering construction. The numerical solution calculation amount of the non-dispersive water wave model is small, the efficiency is high, and the method plays an important role in the simulation of large-scale water wave dynamics, such as tidal motion and the like. However, the model is limited by the theoretical basis of the model, namely the hydrostatic pressure assumption, and the applicability of the model is limited to a certain extent. The simulation distortion of the local flow of steep terrain, complex boundary and hydraulic structure. The dispersive water wave model can make up for the defects of the model, but the calculation efficiency is low, so that the dispersive water wave model is difficult to be applied to numerical simulation of free surface water flow movement with large scale and is mainly used for relevant problem research of laboratory scale.
Disclosure of Invention
The invention provides a water flow simulation method based on a spatial coupling integrated numerical model, aiming at the defects that the numerical model of the current water flow simulation commonly used in the water conservancy industry is a non-dispersive model, the dispersive model is mainly used for small-scale flow simulation, and the two models are independently used. The discrete numerical formats of the control equations are unified, the dispersion mode locally operates, the data exchange is realized by interpolation of the region interfaces by taking the theoretical flow velocity profile as a basic template, and the organic combination of the simulation precision and the calculation efficiency is realized. The invention gives full play to the high efficiency of the non-dispersive water wave model simulation and the high precision of the dispersive water wave model simulation, and expands the application range of the two models by considering the advantages of the two models.
The invention is realized by the following technical scheme:
the invention relates to a water flow simulation method based on a space coupling integrated numerical model, which is characterized in that a numerical model of water wave dynamics is established based on a finite volume method of a non-structural computational grid with a highly-fitted complex boundary; then, dividing the integral calculation domain into a non-dispersive water wave execution region and a dispersive water wave execution region which respectively and independently operate by the spatial region division, wherein different calculation models are adopted in different regions; the integration simulation of the dispersive and non-dispersive water wave models is realized among the areas, namely the area connection through constructing an exchange function; and finally establishing a coupled water wave numerical model for water flow simulation.
The exchange function is preferably a hyperbolic function, so that numerical noise caused by area subdivision is avoided.
The independent operation, namely the non-dispersion water wave model and the dispersion water wave model which are respectively adopted by the non-dispersion water wave execution region and the dispersion water wave execution region, realizes the integrated simulation by a prediction-correction numerical simulation method.
The water flow simulation is that the proportion of the non-hydrostatic model is set through a switch according to different areas of a space calculation domain, so that a mixed model mode is formed, wherein: the numerical simulation universe adopts a dispersion mode calculation, and the dispersion mode only runs in a region where the solitary wave passes through.
The invention relates to a system for realizing the method, which comprises the following steps: a region computational mesh generation unit for generating a region computational mesh generation unit, a pattern recognition unit for a region model, a region data exchange unit, and an overall numerical simulation unit, wherein: the mode identification unit of the area model sets execution areas of the dispersion and non-dispersion models on the basis of the whole computational grid system, the area data exchange unit generates corresponding area data exchange modes according to area interface geometric information, and the whole numerical simulation unit carries out integrated numerical simulation on the basis of area division and condition setting.
Technical effects
The invention integrally solves the technical problems of unified modeling of a dispersion model and a non-dispersion model, integration of numerical simulation of two types of models and bidirectional transmission of regional data in the coupling process of the two types of models.
Compared with the existing dispersion and non-dispersion models which are both independently simulated and are respectively suitable for different engineering requirements, the invention combines the two models into one; the advantages of the two traditional models are considered, the defects are abandoned to a great extent, and the effective combination of simulation precision and efficiency is realized.
Drawings
FIG. 1 is a schematic diagram of an example of high-precision computation mesh space subdivision and synthesis;
in the figure: a is a division of a local calculation domain of a river; b is computational mesh subdivision for highly fitting complex island boundaries; c is a calculation grid of local encryption, wherein an S-shaped line is a preset encryption path; d is an integral calculation grid generated by dividing and combining the calculation domains;
FIG. 2 is a schematic diagram of a spatial combination of dispersive and non-dispersive models;
in the figure: a) dividing a horizontal plane of a calculation domain and setting a model operation area; b) mesh subdivision and region coupling indication of vertical coordinates are carried out;
FIG. 3 is a schematic diagram of an exemplary real-time shifted pattern area application;
FIG. 4 is a schematic view of a flow simulation under a background step terrain;
in the figure: a is a calculation domain; b is a computational grid;
FIG. 5 is a diagram illustrating simulated values of a pressure distribution;
in the figure: a is calculation of a global domain by adopting a dispersion mode, and is marked as a Non-static model; b is that the dispersion mode only runs in the region where the solitary wave passes through, and is marked as Hybrid model;
FIG. 6 is a schematic view of a flow field structure simulation;
in the figure: a is Non-static model; b is a Hybrid model;
FIG. 7 is a schematic flow chart of the present invention.
Detailed Description
As shown in fig. 7, the water flow simulation method of the spatial coupling integrated numerical model relating to the dispersive and non-dispersive water wave models in the present embodiment includes the following steps:
step 1) dividing a complex area into a plurality of blocks: each subarea is respectively set with a solid domain boundary and is dispersed into a line segment unit according to the requirement of spatial resolution, and the boundary discrete forms of adjacent areas are kept consistent; each subregion respectively adopts a lattice generation technology such as a wavefront advancing method, a geometric splitting method and the like to generate an independent space lattice; and combining every two sub-areas, eliminating common edges, unifying the topological sequence of the grid, and finally obtaining the whole computational grid.
In water conservancy projects, particularly oceans, coasts, river watersheds and the like, the numerical simulation calculation domain has large scale, but the space-time scale of the engineering problem needs high resolution. A single computational grid generating program is difficult to meet grid quality requirements, and a block generation-local splicing technology is an effective way for solving the problem. As shown in fig. 1, the calculation grid is a spliced calculation grid from the upper great channel of the Yangtze river basin to the deep line of-50 meters in the east China sea. Meanwhile, by subdividing the space domain, the operation area of the dispersive and non-dispersive water wave model can be set.
Step 2) subdivision and combination of the dispersive and non-dispersive water wave model sub-regions: the dispersive water wave model and the non-dispersive water wave model are set with different space calculating domains separately, and the two models are integrated and coupled. The flow field data between the models is exchanged in real time through the zone interface, and the fixed model zones are schematically divided, as shown in fig. 2. Transition regions are set between the regions, and hyperbolic functions are used for data alternation to increase the smoothness of the data. For a specific problem, the calculation domain of the local dispersion water wave model can be set as a space domain which changes in real time.
As shown in fig. 3, for the simulation of solitary wave propagation, the computational domain of dispersed water waves is adjusted in real time according to the solitary wave motion parameters, i.e., the peak velocity. For space division with fixed space, the operating region of the dispersion model is independently generated into a computational grid, the continuity of a computational grid topological sequence is ensured, and the computational efficiency is improved. For the space division of real-time change, the operating area of the dispersion model is independently generated, a regular grid topological sequence arrangement mode is given, and the calculation efficiency is improved.
The transition region is interpolated by the following method:
Figure BDA0002463396380000031
wherein:
Figure BDA0002463396380000032
for two point function values, ψ (r) is a hyperbolic interpolation function.
Step 3) integrated numerical simulation: the numerical method is based on the Finite Volume Method (FVM), with a high degree of conservation. The numerical format is based on a second-order TVD format, and a numerical simulation calculation program is compiled by an MPI/OpenMP mixed language.
The non-dispersive and dispersive water wave model integrated simulation is based on a prediction-correction method technology, and specifically comprises the following steps:
basic control equation:
Figure BDA0002463396380000033
wherein:
Figure BDA0002463396380000034
which is the fluid motion velocity, p is the pressure,
Figure BDA0002463396380000035
in order to be the acceleration of the gravity,
Figure BDA0002463396380000036
as the earth's rotational speed, upsilon is the kinematic viscosity coefficient of the fluid.
Pressure decomposition: p ═ pH+pnWherein: p is a radical ofHCorresponding to the pressure, p, of the non-dispersed water wavenCorresponding to the pressure of the dispersed water wave.
The prediction-correction method technology comprises the following steps:
estimating flow field calculation, and simulating non-dispersive water wave:
the continuous equation:
Figure BDA0002463396380000037
wherein: zeta is the water level value, Qx,QyAs a variable of the flow flux, Z1,Z2Is a coefficient matrix;
the momentum equation:
Figure BDA0002463396380000041
wherein: a. theix,Gxi,BiRespectively are coefficient matrixes; a. theiy,Gyi,BiRespectively are coefficient matrixes; a. theiz,GziRespectively are coefficient matrixes;
correcting flow field calculation and dispersive water wave simulation:
the momentum equation:
Figure BDA0002463396380000042
wherein: ciIs a coefficient matrix;
the continuous equation:
Figure BDA0002463396380000043
wherein: AP (Access Point)i,k,
Figure BDA0002463396380000044
The indices "n" and "n + 1" of the variables in the above formula represent two different time instants, respectively, for the coefficient matrices.
And thirdly, the simulation of the discrete algebraic equation set is realized by adopting a preprocessed conjugate gradient method (BICGSAB).
Step 4) in order to verify the effectiveness of the present invention, numerical experiments are used to illustrate. Designing a numerical experiment of solitary wave propagation on flat ground, wherein the calculation domain and the calculation grid are shown in figure 3; different regions of the spatial calculation domain, and the occupation ratio of the non-hydrostatic model is set through a switch, so that a mixed model mode is formed, wherein: calculating a numerical simulation universe by adopting a dispersion mode, and marking as a Non-static model; the dispersive mode operates only in the region through which the solitary wave passes, denoted as Hybrid model.
The number of calculation units in the whole calculation domain is 234000, the Non-hydraulic model runs in the whole domain, and the number of occupied units is set to 100%. The Hybrid model only runs in a local area, and the occupied unit number is 22%. The CPU time of the Non-hydraulic model is set to be 100%, and the CPU time of the Hybrid model is calculated to be 51%. The statistics are summarized in the table below. The elapsed time of the CPU indicates the efficiency of the model operation.
Figure BDA0002463396380000045
In order to verify the simulation accuracy of the model, an example of water flowing through the terrain of the rear step is designed for verification. The setting of the two modes is the same as the above example. Fig. 4 shows the computational domain and the computational grid, fig. 5 shows a comparison of the pressure distributions calculated by the two models, and fig. 6 shows a comparison of the flow field structures calculated by the two models. The results show the simulation accuracy of the hybrid model. A comparison of the computational efficiencies of the models is given in the following table, with the variables explained above.
Figure BDA0002463396380000046
Figure BDA0002463396380000051
Compared with the prior art with a single operation mode, namely, two types of models can only be independently applied; according to the invention, different areas of a spatial calculation domain are set by a switch to set the proportion of a non-hydrostatic model, so that a mixed model mode is formed, the integrated simulation is realized as a main technical key point, and the stability of numerical calculation is ensured by an area data exchange mode. The invention obviously improves the simulation precision of the non-dispersion model and reduces the CPU time consumption of the dispersion model; the integrated integral simulation of the large scale of the watershed and the small scale of the engineering in the hydraulic engineering improves the applicability of the model.
The foregoing embodiments may be modified in many different ways by those skilled in the art without departing from the spirit and scope of the invention, which is defined by the appended claims and all changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims (3)

1. A water flow simulation method based on a space coupling integrated numerical model is characterized in that a numerical model of water wave dynamics is established based on a finite volume method of a non-structural computational grid with a highly fitting complex boundary; then, dividing the integral calculation domain into a non-dispersive water wave execution region and a dispersive water wave execution region which respectively and independently operate by the spatial region division, wherein different calculation models are adopted in different regions; the integration simulation of the dispersive and non-dispersive water wave models is realized among the areas, namely the area connection through constructing an exchange function; finally, establishing a coupled water wave numerical model for water flow simulation;
the exchange function is a hyperbolic function, so that numerical noise caused by area subdivision is avoided;
the independent operation, namely the non-dispersive water wave model and the dispersive water wave model which are respectively adopted by the non-dispersive water wave execution region and the dispersive water wave execution region, realizes the integrated simulation by a prediction-correction numerical simulation method, and specifically comprises the following steps:
step 1) dividing a complex area into a plurality of blocks: each subarea is respectively set with a solid domain boundary and is dispersed into a line segment unit according to the requirement of spatial resolution, and the boundary discrete forms of adjacent areas are kept consistent; each subregion respectively adopts a lattice generation technology of a wavefront advancing method and a geometric splitting method to generate an independent space lattice; combining every two sub-areas, eliminating common edges, unifying grid topological sequences and finally obtaining an integral computing grid;
step 2) subdivision and combination of the dispersive and non-dispersive water wave model sub-regions: different space calculation domains are respectively set for a dispersive water wave model and a non-dispersive water wave model, the two models are integrally simulated and mutually coupled, flow field data between the models are exchanged in real time through a domain interface, the fixed model regions are schematically divided, transition regions are set between the regions, and the data are further increased in smoothness by adopting a hyperbolic function;
step 3) integrated numerical simulation: the numerical method is based on a finite volume method, the numerical format is based on a second-order TVD format, and a numerical simulation calculation program is compiled in an MPI/OpenMP mixed language;
the coupled water wave numerical model for water flow simulation comprises:
basic control equation:
Figure FDA0002763980020000011
wherein:
Figure FDA0002763980020000012
which is the fluid motion velocity, p is the pressure,
Figure FDA0002763980020000013
in order to be the acceleration of the gravity,
Figure FDA0002763980020000014
is the earth rotation speed, upsilon is the motion viscosity coefficient of the fluid;
pressure decomposition: p ═ pH+pnWherein: p is a radical ofHCorresponding to the pressure, p, of the non-dispersed water wavenA pressure corresponding to the dispersed water wave;
the prediction-correction numerical simulation method specifically comprises the following steps:
estimating flow field calculation, and simulating non-dispersive water wave:
the continuous equation:
Figure FDA0002763980020000015
wherein: zeta is the water level value, Qx,QyAs a variable of the flow flux, Z1,Z2Is a coefficient matrix;
the momentum equation:
Figure FDA0002763980020000021
wherein: a. theix,Gxi,BiRespectively are coefficient matrixes; a. theiy,Gyi,BiRespectively are coefficient matrixes; a. theiz,GziRespectively are coefficient matrixes;
correcting flow field calculation and dispersive water wave simulation:
the momentum equation:
Figure FDA0002763980020000022
wherein: ciIs a coefficient matrix;
the continuous equation:
Figure FDA0002763980020000023
wherein: AP (Access Point)i,k,
Figure FDA0002763980020000024
Respectively are coefficient matrixes, and superscripts n and n +1 respectively represent two different moments;
and thirdly, the simulation of the discrete algebraic equation set is realized by adopting a preprocessed conjugate gradient method.
2. The water flow simulation method according to claim 1, wherein the water flow simulation is performed by setting the proportion of the non-hydrostatic model by a switch according to different regions of the spatial computation domain, thereby forming a mixed model mode, wherein: the numerical simulation universe adopts a dispersion mode calculation, and the dispersion mode only runs in a region where the solitary wave passes through.
3. A system for implementing the water flow simulation method of claim 1 or 2, comprising: a region computational mesh generation unit for generating a region computational mesh generation unit, a pattern recognition unit for a region model, a region data exchange unit, and an overall numerical simulation unit, wherein: the mode identification unit of the area model sets execution areas of the dispersion and non-dispersion models on the basis of the whole computational grid system, the area data exchange unit generates corresponding area data exchange modes according to area interface geometric information, and the whole numerical simulation unit carries out integrated numerical simulation on the basis of area division and condition setting.
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