A method, device, equipment and medium for determining vorticity and velocity in large eddy simulation

Abstract

The present application discloses a method, device, equipment and medium for determining vorticity and velocity of large eddy simulation, which is applied to the field of vortex dynamics technology, including: obtaining the target flow field velocity and target vorticity at the previous moment, the target flow field velocity includes the flow field velocity obtained by using a grid filter and a test filter, and the target vorticity includes the vorticity obtained by using a grid filter and a test filter; calculating the analytical vorticity flux based on the target flow field velocity and the target vorticity; calculating the target first physical quantity based on the target vorticity; calculating the eddy viscosity coefficient based on the analytical vorticity flux and the target first physical quantity; determining the target vorticity at the next moment based on the eddy viscosity coefficient and the vorticity transport equation; calculating the target flow field velocity at the next moment based on the flow field velocity obtained by filtering the grid filter at the previous moment and the vorticity obtained by filtering the grid filter at the next moment. In this way, the eddy viscosity coefficient can be adaptively calculated, thereby accurately determining the vorticity and velocity of the flow field.

Description

Technical Field

[0001] The present application relates to the technical field of vortex dynamics, and in particular to a method, device, equipment and medium for determining vorticity and velocity in large eddy simulation. Background Art

[0002] Studies have found that the core physical process of the evolution of multi-scale turbulence is the dynamic evolution of multi-scale vortex structures. Therefore, vortex dynamics has received increasing attention in recent years. At present, in the large eddy simulation scenario, how to accurately determine the vorticity and velocity of the flow field is an urgent problem to be solved. Summary of the invention

[0003] In view of this, the purpose of this application is to provide a method, device, equipment and medium for determining vorticity and velocity of large eddy simulation, which can accurately determine the vorticity and velocity of the flow field. The specific scheme is as follows:

[0004] In a first aspect, the present application discloses a method for determining vorticity and velocity in large eddy simulation, comprising:

[0005] Obtaining a target flow field velocity at a previous moment and a target vorticity at a previous moment, wherein the target flow field velocity includes a flow field velocity obtained by filtering with a grid filter of large eddy simulation and a flow field velocity obtained by filtering with a test filter, and the target vorticity includes a vorticity obtained by filtering with a grid filter of large eddy simulation and a vorticity obtained by filtering with a test filter, and the test filter is a filter having a grid size larger than a grid size of the grid filter;

[0006] Calculating an analytical vorticity flux based on the target flow field velocity and the target vorticity, wherein the analytical vorticity flux characterizes the contribution of a flow structure having a scale between a filter width of the grid filter and a filter width of the test filter to vorticity transport;

[0007] Calculate a target first physical quantity based on the target vorticity, the target first physical quantity includes a first physical quantity obtained by filtering using the grid filter and a first physical quantity obtained by filtering using the test filter, wherein the first physical quantity is a symmetric tensor representing a spatial variation of a vorticity field;

[0008] The eddy viscosity coefficient is calculated based on the analytical vortex flux and the target first physical quantity and using an eddy viscosity coefficient calculation formula, wherein the eddy viscosity coefficient calculation formula is established based on a pseudo-eddy energy power conservation relationship of a flow structure whose scale is between the filter width of the grid filter and the filter width of the test filter;

[0009] A vorticity transport equation is closed based on the eddy viscosity coefficient, and a target vorticity at a next moment corresponding to the previous moment is determined based on the vorticity transport equation;

[0010] Based on the flow field velocity obtained by filtering using a grid filter of large eddy simulation at the previous moment and the vorticity obtained by filtering using a grid filter of large eddy simulation at the next moment corresponding to the previous moment, the target flow field velocity at the next moment corresponding to the previous moment is calculated.

[0011] Optionally, the eddy viscosity coefficient calculation formula is:

[0012] ;

[0013] in, is the eddy viscosity coefficient, To resolve the vorticity flux, , , represents the first physical quantity obtained by filtering using the grid filter, To test the filter width of the filter, is the filter width of the grid filter, represents the norm of the first physical quantity obtained by filtering using the test filter, represents the first physical quantity obtained by filtering using the test filter, represents the norm of the first physical quantity obtained by filtering using the grid filter, Represents the filter processing of the test filter.

[0014] Optionally, when the preset flow field uniformity condition is met, the eddy viscosity coefficient calculation formula is:

[0015] ;

[0016] in, is the eddy viscosity coefficient, To resolve the vorticity flux, , , represents the first physical quantity obtained by filtering using the grid filter, To represent the filter width of the grid filter, represents the norm of the first physical quantity obtained by filtering using the test filter, represents the first physical quantity obtained by filtering using the test filter, represents the norm of the first physical quantity obtained by filtering using the grid filter, Represents the filtering process of the test filter.

[0017] Optionally, the calculating the analytical vorticity flux based on the target flow field velocity and the target vorticity includes:

[0018] The analytical vortex flux calculation formula is used to calculate the analytical vortex flux based on the target flow field velocity and the target vortex; the analytical vortex flux calculation formula is:

[0019] ;

[0020] in, To resolve the vorticity flux, , is the flow field velocity obtained by filtering with a grid filter using large eddy simulation, , is the flow field velocity obtained by filtering using the test filter, , is the vorticity obtained by filtering using the grid filter of large eddy simulation, , is the vorticity obtained by filtering using the test filter, Represents the filtering process of the test filter, and i and j represent different directions.

[0021] Optionally, calculating a target first physical quantity based on the target vorticity includes:

[0022] The first physical quantity is determined based on the target vorticity using a preset first physical quantity calculation formula; the preset first physical quantity calculation formula is:

[0023] , ;

[0024] in, represents the first physical quantity after filtering by the grid filter, , represents the vorticity obtained by filtering using a grid filter, Represents the first physical quantity after the test filter is filtered. , represents the vorticity obtained by filtering using the test filter, , is the distance vector, i and j represent different directions.

[0025] Optionally, the vorticity transport equation is:

[0026] ;

[0027] in, is the vorticity obtained by filtering using the grid filter of large eddy simulation, is the flow field velocity obtained by filtering with a grid filter using large eddy simulation, is the eddy viscosity coefficient, t is the time, is the distance vector, is the filter width of the grid filter, represents the norm of the first physical quantity obtained by filtering using the grid filter, represents the first physical quantity after filtering by the grid filter, represents the kinematic viscosity coefficient, , Represents the vorticity obtained by filtering using a grid filter, and i and j represent different directions.

[0028] Optionally, the calculating the target flow field velocity at the next moment corresponding to the previous moment based on the flow field velocity obtained by filtering using a grid filter using large eddy simulation at the previous moment and the vorticity obtained by filtering using a grid filter using large eddy simulation at the next moment corresponding to the previous moment includes:

[0029] The stream function vector is updated by using a first preset formula and based on the vorticity obtained by filtering the grid filter using large eddy simulation at the next moment corresponding to the previous moment; the first preset formula is:

[0030] ;

[0031] in, is the stream function vector, is the distance vector, is the vorticity obtained by filtering with a grid filter using large eddy simulation, i and j represent different directions;

[0032] The velocity potential function is updated using the second preset formula and according to the flow field velocity obtained by filtering the grid filter using the large eddy simulation at the previous moment; the second preset formula is:

[0033] ;

[0034] in, is the velocity potential function, is the flow field velocity obtained by filtering the grid filter using large eddy simulation at the previous moment;

[0035] The flow field velocity obtained by filtering the grid filter using large eddy simulation at the next moment corresponding to the previous moment is calculated using a third preset formula based on the updated stream function vector and the velocity potential function; the third preset formula is:

[0036] ;

[0037] in, is the substitution symbol, is the stream function vector, is the distance vector, The flow field velocity at the next moment is obtained by filtering the grid filter using large eddy simulation;

[0038] The flow field velocity at the next moment obtained by filtering using the test filter is calculated based on the flow field velocity obtained by filtering using the grid filter of the large eddy simulation at the next moment.

[0039] In a second aspect, the present application discloses a device for determining vorticity and velocity of large eddy simulation, comprising:

[0040] A velocity and vorticity acquisition module, used to acquire a target flow field velocity and a target vorticity at a previous moment, wherein the target flow field velocity includes a flow field velocity obtained by filtering a grid filter of large eddy simulation and a flow field velocity obtained by filtering a test filter, and the target vorticity includes a vorticity obtained by filtering a grid filter of large eddy simulation and a vorticity obtained by filtering a test filter, and the test filter is a filter having a grid size larger than a grid size of the grid filter;

[0041] An analytical vorticity flux calculation module, used for calculating an analytical vorticity flux based on the target flow field velocity and the target vorticity, wherein the analytical vorticity flux characterizes the contribution of a flow structure having a scale between a filter width of the grid filter and a filter width of the test filter to vorticity transport;

[0042] A first physical quantity calculation module, used for calculating a target first physical quantity based on the target vorticity, wherein the target first physical quantity includes a first physical quantity obtained by filtering using the grid filter and a first physical quantity obtained by filtering using the test filter, wherein the first physical quantity is a symmetric tensor representing a spatial variation of a vorticity field;

[0043] An eddy viscosity coefficient calculation module, used for calculating the eddy viscosity coefficient based on the analytical vortex flux, the target first physical quantity and using an eddy viscosity coefficient calculation formula, wherein the eddy viscosity coefficient calculation formula is established based on a pseudo-eddy energy power conservation relationship of a flow structure whose scale is between the filter width of the grid filter and the filter width of the test filter;

[0044] A target vorticity calculation module, used for closing the vorticity transport equation based on the eddy viscosity coefficient, and determining the target vorticity at the next moment corresponding to the previous moment based on the vorticity transport equation;

[0045] The flow field velocity calculation module is used to calculate the target flow field velocity at the next moment corresponding to the previous moment based on the flow field velocity obtained by filtering using a grid filter using large eddy simulation at the previous moment and the vorticity obtained by filtering using a grid filter using large eddy simulation at the next moment corresponding to the previous moment.

[0046] In a third aspect, the present application discloses an electronic device, including a memory and a processor, wherein:

[0047] The memory is used to store the computer program;

[0048] The processor is used to execute the computer program to implement the aforementioned method for determining vorticity and velocity of large eddy simulation.

[0049] In a fourth aspect, the present application discloses a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the aforementioned method for determining vorticity and velocity of large eddy simulation.

[0050] It can be seen from the above scheme that the present application provides a method for determining the vorticity and velocity of a large eddy simulation, including: obtaining a target flow field velocity and a target vorticity at the previous moment, wherein the target flow field velocity includes the flow field velocity obtained by filtering with a grid filter of a large eddy simulation and the flow field velocity obtained by filtering with a test filter, and the target vorticity includes the vorticity obtained by filtering with a grid filter of a large eddy simulation and the vorticity obtained by filtering with a test filter, and the test filter is a filter with a grid size larger than the grid size of the grid filter; calculating an analytical vorticity flux based on the target flow field velocity and the target vorticity, wherein the analytical vorticity flux characterizes the contribution of a flow structure with a scale between the filter width of the grid filter and the filter width of the test filter to the vorticity transport; calculating a target first physical quantity based on the target vorticity, and the target first physical quantity includes using A first physical quantity filtered by the grid filter and a first physical quantity filtered by the test filter, wherein the first physical quantity is a symmetric tensor representing the spatial variation of the vortex field; the eddy viscosity coefficient is calculated based on the analytical vortex flux, the target first physical quantity and using an eddy viscosity coefficient calculation formula, wherein the eddy viscosity coefficient calculation formula is established based on the pseudo-vortex energy-power conservation relationship of a flow structure whose scale is between the filter width of the grid filter and the filter width of the test filter; a vortex transport equation is closed based on the eddy viscosity coefficient, and a target vortex at a next moment corresponding to the previous moment is determined based on the vortex transport equation; a target flow field velocity at a next moment corresponding to the previous moment is calculated based on the flow field velocity filtered by the grid filter using large eddy simulation at the previous moment and the vortex filtered by the grid filter using large eddy simulation at the next moment corresponding to the previous moment.

[0051] It can be seen that the present application is based on the pseudo-eddy energy power conservation relationship of the flow structure whose scale is between the filtering width of the grid filter and the filtering width of the test filter. According to the local flow characteristics of the flow field, the eddy viscosity coefficient can be adaptively calculated, thereby accurately determining the vorticity and velocity of the flow field.

[0052] Correspondingly, the vorticity and velocity device, equipment and readable storage medium for large eddy simulation provided by the present application also have the above-mentioned technical effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0054] Figure 1 A flow chart of a method for determining vorticity and velocity in a large eddy simulation provided in an embodiment of the present application;

[0055] Figure 2 A grid schematic diagram provided for an embodiment of the present application;

[0056] Figure 3 A schematic diagram for determining a vortex transport equation provided in an embodiment of the present application;

[0057] Figure 4 A schematic diagram of the structure of a device for determining vorticity and velocity in large eddy simulation provided in an embodiment of the present application;

[0058] Figure 5 A structural diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0060] At present, it is urgent to independently develop fluid industry software. For industrial-scale fluid mechanics simulation problems, large eddy simulation is a commonly used technology, which can ensure that the fluid solver accurately depicts multi-scale turbulence and greatly reduce the amount of calculation. It is an important technology for modern fluid simulation software. However, the traditional large eddy simulation method is based on the Navier-Stokes equation, and the large eddy simulation method developed in the embodiment of the present application is based on the vortex dynamics equation, which can better depict the multi-scale turbulent vortex structure.

[0061] Dynamics has received more and more attention in recent years because studies have found that the core physical process of the evolution of multi-scale turbulence is the dynamic evolution of multi-scale vortex structures. Therefore, based on the direct numerical simulation solver of vortex dynamics, this application further derives the basic equations of large eddy simulation based on the vortex dynamics equations, and obtains the adaptive expression of eddy viscosity coefficient of large eddy simulation of vortex dynamics through the principle of conservation of energy. Based on this, a large eddy simulation solver of vortex dynamics is developed for industrial-scale multi-scale turbulence numerical simulation.

[0062] See also Figure 1 As shown, the embodiment of the present application discloses a method for determining vorticity and velocity of large eddy simulation, comprising:

[0063] Step S11: Obtain the target flow field velocity and the target vorticity at the previous moment, wherein the target flow field velocity includes the flow field velocity obtained by filtering with a grid filter of large eddy simulation and the flow field velocity obtained by filtering with a test filter, and the target vorticity includes the vorticity obtained by filtering with a grid filter of large eddy simulation and the vorticity obtained by filtering with a test filter, and the test filter is a filter having a grid size larger than the grid size of the grid filter.

[0064] Step S12: Calculate the analytical vorticity flux based on the target flow field velocity and the target vorticity, wherein the analytical vorticity flux characterizes the contribution of the flow structure with a scale between the filter width of the grid filter and the filter width of the test filter to the vorticity transport.

[0065] In this embodiment, the analytical vortex flux calculation formula can be used to calculate the analytical vortex flux based on the target flow field velocity and the target vorticity; the analytical vortex flux calculation formula is:

[0066] ;

[0067] in, To resolve the vorticity flux, , is the flow field velocity obtained by filtering with a grid filter using large eddy simulation, , is the flow field velocity obtained by filtering using the test filter, , is the vorticity obtained by filtering using the grid filter of large eddy simulation, , is the vorticity obtained by filtering using the test filter, Represents the filtering process of the test filter, and i and j represent different directions.

[0068] Step S13: Calculate a target first physical quantity based on the target vorticity, wherein the target first physical quantity includes a first physical quantity filtered by the grid filter and a first physical quantity filtered by the test filter, wherein the first physical quantity is a symmetric tensor representing the spatial variation of the vorticity field.

[0069] In this embodiment, a preset first physical quantity calculation formula can be used to determine the first physical quantity based on the target vorticity; the preset first physical quantity calculation formula is:

[0070] , ;

[0071] in, represents the first physical quantity after filtering by the grid filter, , represents the vorticity obtained by filtering using a grid filter, Represents the first physical quantity after the test filter is filtered. , represents the vorticity obtained by filtering using the test filter, , is the distance vector, i and j represent different directions.

[0072] Step S14: Calculate the eddy viscosity coefficient based on the analytical vortex flux, the target first physical quantity and using the eddy viscosity coefficient calculation formula, wherein the eddy viscosity coefficient calculation formula is established based on the pseudo-vortex energy power conservation relationship of a flow structure whose scale is between the filtering width of the grid filter and the filtering width of the test filter.

[0073] In this embodiment, the eddy viscosity coefficient calculation formula is:

[0074] ;

[0075] in, is the eddy viscosity coefficient, To resolve the vorticity flux, , , represents the first physical quantity obtained by filtering using the grid filter, To test the filter width, is the filter width of the grid filter, represents the norm of the first physical quantity obtained by filtering using the test filter, represents the first physical quantity obtained by filtering using the test filter, represents the norm of the first physical quantity obtained by filtering using the grid filter, Represents the filter processing of the test filter. This embodiment uses the Einstein index form to represent the first physical quantity. In the Einstein summation convention, if an index (which can be a subscript or a superscript) appears twice in the same item, it means that the index is traversed and summed. Such indicators are called dummy indicators because their specific names are not important. What is important is that they represent the summation operation. Indicators that appear only once are called free indicators. They will not be summed, but retained as indices in the final expression. Physical quantities with subscripts mn and pq and physical quantities with subscript ij have the same meaning. , .

[0076] Furthermore, when the preset flow field uniformity condition is met, the eddy viscosity coefficient calculation formula is:

[0077] ;

[0078] in, is the eddy viscosity coefficient, To resolve the vorticity flux, , , represents the first physical quantity obtained by filtering using the grid filter, To represent the filter width of the grid filter, represents the norm of the first physical quantity obtained by filtering using the test filter, represents the first physical quantity obtained by filtering using the test filter, represents the norm of the first physical quantity obtained by filtering using the grid filter, Represents the filtering process of the test filter.

[0079] That is, for problems with uniform flow fields and simple geometric shapes, this embodiment can use a uniform grid, and take the filter width of the test filter as twice the filter width of the grid filter. The eddy viscosity coefficient calculation formula can be simplified to the above formula, thereby reducing the amount of calculation. Uniform grids also mean that the grid size is consistent. A uniform flow field can be understood as a flow field without a large velocity gradient and no drastic changes. The solver determines the grid division method based on experience and specific problems.

[0080] Step S15: closing the vorticity transport equation based on the eddy viscosity coefficient, and determining the target vorticity at the next moment corresponding to the previous moment based on the vorticity transport equation.

[0081] In this embodiment, the vortex transport equation is:

[0082] ;

[0083] in, is the vorticity obtained by filtering using the grid filter of large eddy simulation, is the flow field velocity obtained by filtering with a grid filter using large eddy simulation, is the eddy viscosity coefficient, t is the time, is the distance vector, is the filter width of the grid filter, represents the norm of the first physical quantity obtained by filtering using the grid filter, represents the first physical quantity after filtering by the grid filter, represents the kinematic viscosity coefficient, , Represents the vorticity obtained by filtering using a grid filter, and i and j represent different directions.

[0084] Step S16: Based on the flow field velocity obtained by filtering using a grid filter of large eddy simulation at the previous moment and the vorticity obtained by filtering using a grid filter of large eddy simulation at the next moment corresponding to the previous moment, calculate the target flow field velocity at the next moment corresponding to the previous moment.

[0085] This embodiment can use a first preset formula and update the stream function vector based on the vorticity obtained by filtering the grid filter using large eddy simulation at the next moment corresponding to the previous moment; the first preset formula is:

[0086] ;

[0087] in, is the stream function vector, is the distance vector, is the vorticity obtained by filtering with a grid filter using large eddy simulation, i and j represent different directions;

[0088] The velocity potential function is updated using the second preset formula and according to the flow field velocity obtained by filtering the grid filter using the large eddy simulation at the previous moment; the second preset formula is:

[0089] ;

[0090] in, is the velocity potential function, is the flow field velocity obtained by filtering the grid filter using large eddy simulation at the previous moment;

[0091] The flow field velocity obtained by filtering the grid filter using large eddy simulation at the next moment corresponding to the previous moment is calculated using a third preset formula based on the updated stream function vector and the velocity potential function; the third preset formula is:

[0092] ;

[0093] in, is the substitution symbol, is the stream function vector, is the distance vector, The flow field velocity obtained by filtering using the grid filter of large eddy simulation at the next moment.

[0094] The flow field velocity obtained by filtering using the test filter at the next moment is calculated based on the flow field velocity obtained by filtering using the grid filter using large eddy simulation at the next moment. Specifically, the flow field velocity obtained by filtering using the grid filter using large eddy simulation at the next moment is filtered using the test filter to obtain the flow field velocity obtained by filtering using the test filter at the next moment.

[0095] It should be pointed out that the core idea of ​​Large Eddy Simulation (LES) is to decompose the flow into large-scale resolvable flow and small-scale flow that needs to be approximated by the model through spatial filtering. Among them, large scale and small scale are relative concepts, which are related to the problem to be solved, the part of concern, the size of the computational domain, etc., and there is no absolute value. The size scale depends on the size of the filter function. The filter function filters out the small scale, and retains the large scale. The implementation of spatial filtering usually adopts convolution operation, using the filter function (filter) With physical quantity Perform convolution calculations to obtain physical quantities on a coarser grid :

[0096] (1);

[0097] The filter function in large eddy simulation is a tool used to separate large-scale vortices in the fluid field (the part that we want to simulate directly) from small-scale vortices (the part that needs to be simulated through a subgrid model). The filter function is usually a local operation, which can be a box filter, a Gaussian filter, or a hat filter. Among them, the physical quantity is a general concept, and any physical quantity can be obtained by filtering to obtain the large-scale part. Among them, the grid size of the coarser grid is based on the specific problem to be solved and is controlled by the size of the filter.

[0098] The vorticity transport equation for incompressible viscous flow is:

[0099] (2);

[0100] in is the vorticity, t is the time, represents the kinematic viscosity coefficient, For speed, is the gradient operator. Rewrite the above equation into the following tensor form:

[0101] (3);

[0102] in, Indicates speed, is the distance vector, i and j represent different directions. In this embodiment, the vectors are all represented by Einstein index, and the subscripts j=1, 2, and 3 represent three different directions. The conservation form of the vortex transport equation is further derived below. The left side of the above equation can be written as:

[0103] (4);

[0104] For the vorticity field, it is a tubular vector field that satisfies:

[0105] (5);

[0106] And, for incompressible flow, it satisfies:

[0107] (6);

[0108] Therefore, the third and fifth terms on the right side of the equal sign in formula (4) are zero. Finally, the nonlinear terms on the left side of the equal sign in equation (3) (i.e., the second and third terms) can be written in a conservation form, and the conservation form of the vortex transport equation for incompressible viscous flow is obtained as follows:

[0109] (7);

[0110] Using a grid filter Filtering equation (7) yields the following filtering equation:

[0111] (8);

[0112] In the above formula, the physical quantity with an upper horizontal line represents the large-scale flow result after filtering, which can be directly calculated. and speed Decompose into resolvable large-scale components ( and ), and the unresolved small-scale part ( and ):

[0113] (9);

[0114] (10);

[0115] Therefore, the second term in equation (8) It can be expanded into the following form:

[0116] (11);

[0117] When the filter function is operated by the Reynolds operator, ,in is any unresolved small-scale physical quantity.

[0118] The Reynolds operator satisfies the operation rules: , , The operation operator of . , is an arbitrary physical quantity, and the upper horizontal line represents the result of the operator.

[0119] Therefore, the second and third terms on the right side of the equal sign in the above formula satisfy:

[0120] (12);

[0121] (13);

[0122] At this time, formula (11) can be simplified as:

[0123] (14);

[0124] Similarly, there are:

[0125] (15);

[0126] definition for:

[0127] (16);

[0128] When the filter operator is the Reynolds operator, the last equal sign in the above equation holds. Substituting into the filtering equation (8), the filtered vortex transport equation is as follows:

[0129] (17);

[0130] Move the third term in the above equation to the right side and expand it to get:

[0131] (18);

[0132] From formula (5), we can see that the third term on the right side of the equal sign is zero. Finally, the simplified filtered vortex transport equation is as follows:

[0133] (19);

[0134] It shows the influence of small-scale structures smaller than the filter scale on vorticity transport. Large eddy simulation can only directly calculate large-scale flows, so it is necessary to introduce a model to approximate the contribution of small-scale flow structures. Here, the Smagorinsky model is used in a similar form to viscous stress based on the eddy viscosity assumption. The mathematical expression for modeling is:

[0135] (20);

[0136] in, is the filter width, , , is the eddy viscosity coefficient. Dimensional analysis is performed on both sides of the equation to verify its correctness, and the results are as follows:

[0137] (twenty one);

[0138] L represents distance, T represents time, and formula (21) represents the alignment of the dimensions on both sides of the equal sign in formula (19). In order to close the filtered vorticity transport equation obtained above, the eddy viscosity coefficient needs to be given This method is based on the model proposed by Germano in 1991 to derive the eddy viscosity coefficient , this method can adaptively calculate The specific process of adaptively calculating the eddy viscosity coefficient is given below.

[0139] In addition to using a grid filter, the present invention also uses a grid filter. In addition, the test filter (testfilter) is introduced The test filter grid size is larger than the grid filter grid size. The selection of filters can be the same or different, which does not affect the expression of the formula. Final definition: .

[0140] The grids for direct numerical simulation (DNS), grid filters for large eddy simulation (LES), and test filters are as follows: Figure 2 shown. Figure 2A grid schematic diagram provided for an embodiment of the present application, wherein the gray grid represents the DNS grid, which can resolve all scale structures in the flow; the blue grid represents the grid filter grid of the LES, which is larger than the DNS grid, and therefore can only resolve large-scale structures in the flow field. The grid of the test filter is shown by the red dotted line (here the test filter filter size is twice the grid filter size as an example). The result after the test filter processing can be obtained by averaging the results of the grid filter processing. For example, the value after the test filter at the red node in the figure can be obtained by weighted averaging the results at the nine grid point positions defined by the red dotted line.

[0141] Similarly, using Filtering the vorticity transport equation yields the following equation:

[0142] (twenty two);

[0143] In this application, physical quantities with upper horizontal lines and upper wavy lines, such as (f is an arbitrary physical quantity), which represents the large-scale flow result after the test filter is filtered. is a user-defined physical quantity, and its expression is:

[0144] (twenty three);

[0145] Similarly, when the filter operator is the Reynolds operator, the last equal sign in the above equation holds. Definition for:

[0146] (twenty four);

[0147] This term represents the scale between the grid filter width and test filter width The contribution of the flow structure between to the vorticity transport. The expression of contains only the filtered physical quantities.

[0148] Using the above model, that is, formula (20), and The models are as follows:

[0149] (25);

[0150] (26);

[0151] Substituting formula (25) (26) into formula (24), we obtain:

[0152] (27);

[0153] Dimensional analysis on both sides of the equal sign in the above formula yields:

[0154] (28);

[0155] The dimensions on both sides of the equal sign in the above formula are the pseudo-vortex energy power, which shows that, at the physical level, formula (27) reflects the scale between the grid filter width and test filter width The pseudo-vortex energy power of the flow structure is conserved.

[0156] Finally, the eddy viscosity coefficient is obtained The expression is:

[0157] (29);

[0158] This expression only contains the physical quantity after filtering, so equation (19) is closed. And the eddy viscosity coefficient calculated by this method is It can make adaptive adjustments according to the local flow characteristics of the flow field, thereby improving the adaptability of the model to different flow conditions.

[0159] For three-dimensional problems, if the flow field is uniform (e.g., uniform velocity, no large velocity gradient), and the geometry is simple, a uniform grid is used, that is, , ; Take the test filter width as twice the grid filter width, that is , where the subscript i represents the grid direction, we have:

[0160] (30);

[0161] (31);

[0162] Therefore, the eddy viscosity coefficient It can also be expressed as:

[0163] (32);

[0164] The filtered vortex transport equation can finally be expressed as:

[0165] (33);

[0166] For example, see Figure 3 As shown, Figure 3A schematic diagram for determining a vortex transport equation provided in an embodiment of the present application.

[0167] Furthermore, in the process of determining the vorticity and velocity, each iterative calculation process is as follows (the upper right script indicates the time step):

[0168] First, get the flow field velocity at the previous moment , and vorticity , ;

[0169] Calculated by formula (24) , , ;

[0170] The eddy viscosity coefficient is calculated according to formula (29): ;

[0171] Solve equation (33) to calculate the vorticity at the next moment ;

[0172] According to the vorticity at the next moment Update stream function vector ;

[0173] ;

[0174] Update the velocity potential function according to the velocity at the previous moment ;

[0175] ;

[0176] Update the flow field velocity at the next moment ;

[0177] ;

[0178] Through The test filter is further used to filter it.

[0179] This embodiment is based on the model proposed by Germano in 1991, and the control equations for numerical solution of large eddy simulation of vortex transport are derived. The eddy viscosity coefficient of large eddy simulation of eddy dynamics is adaptive and does not need to be given in advance. Based on this, independent source code simulation software for numerical simulation of large eddy simulation of eddy dynamics is developed to realize independent control of independent source code software, and the source code software can be parallel calculated by CPU (i.e. Central Processing Unit).

[0180] This application achieves a breakthrough from 0 to 1 and develops a numerical solver for large eddy simulation of incompressible fluids in vortex dynamics. The traditional large eddy simulation solver is based on the Navier-Stokes equations, and this application is based on the vortex dynamics equations. The large eddy simulation solver based on the vortex dynamics equations can better characterize the vortex structure of turbulence. At the same time, the use of the large eddy simulation solver of vortex dynamics can ensure the analysis of multi-scale turbulence while greatly reducing the amount of calculation, realizing the solution of turbulence problems on an industrial scale.

[0181] It can be seen that the embodiment of the present application is based on the pseudo-eddy energy power conservation relationship of the flow structure whose scale is between the filtering width of the grid filter and the filtering width of the test filter. According to the local flow characteristics of the flow field, the eddy viscosity coefficient can be adaptively calculated, thereby accurately determining the vorticity and velocity of the flow field.

[0182] See also Figure 4 As shown, the embodiment of the present application discloses a device for determining vorticity and velocity of large eddy simulation, comprising:

[0183] A velocity and vorticity acquisition module 11 is used to acquire a target flow field velocity and a target vorticity at a previous moment, wherein the target flow field velocity includes a flow field velocity obtained by filtering a grid filter of a large eddy simulation and a flow field velocity obtained by filtering a test filter, and the target vorticity includes a vorticity obtained by filtering a grid filter of a large eddy simulation and a vorticity obtained by filtering a test filter, wherein the test filter is a filter having a grid size larger than a grid size of the grid filter;

[0184] An analytical vorticity flux calculation module 12 is used to calculate an analytical vorticity flux based on the target flow field velocity and the target vorticity, wherein the analytical vorticity flux characterizes the contribution of a flow structure having a scale between a filter width of the grid filter and a filter width of the test filter to vorticity transport;

[0185] A first physical quantity calculation module 13, used for calculating a target first physical quantity based on the target vorticity, wherein the target first physical quantity includes a first physical quantity obtained by filtering using the grid filter and a first physical quantity obtained by filtering using the test filter, wherein the first physical quantity is a symmetric tensor representing a spatial variation of a vorticity field;

[0186] An eddy viscosity coefficient calculation module 14 is used to calculate the eddy viscosity coefficient based on the analytical vortex flux and the target first physical quantity using an eddy viscosity coefficient calculation formula, wherein the eddy viscosity coefficient calculation formula is established based on a pseudo-eddy energy power conservation relationship of a flow structure whose scale is between the filter width of the grid filter and the filter width of the test filter;

[0187] A target vorticity calculation module 15 is used to close the vorticity transport equation based on the eddy viscosity coefficient, and determine the target vorticity at the next moment corresponding to the previous moment based on the vorticity transport equation;

[0188] The flow field velocity calculation module 16 is used to calculate the target flow field velocity at the next moment corresponding to the previous moment based on the flow field velocity obtained by filtering using a grid filter using large eddy simulation at the previous moment and the vorticity obtained by filtering using a grid filter using large eddy simulation at the next moment corresponding to the previous moment.

[0189] In an optional implementation, the eddy viscosity coefficient calculation module 14 is specifically used for:

[0190] The eddy viscosity coefficient is calculated based on the analytical vortex flux and the target first physical quantity using the eddy viscosity coefficient calculation formula. In this embodiment, the eddy viscosity coefficient calculation formula is:

[0191] ;

[0192] in, is the eddy viscosity coefficient, To resolve the vorticity flux, , , represents the first physical quantity obtained by filtering using the grid filter, To test the filter width, is the filter width of the grid filter, represents the norm of the first physical quantity obtained by filtering using the test filter, represents the first physical quantity obtained by filtering using the test filter, represents the norm of the first physical quantity obtained by filtering using the grid filter, Represents the filter processing of the test filter.

[0193] When the preset flow field uniformity condition is met, the eddy viscosity coefficient calculation formula is:

[0194] ;

[0195] in, is the eddy viscosity coefficient, To resolve the vorticity flux, , , represents the first physical quantity obtained by filtering using the grid filter, is the filter width of the grid filter, represents the norm of the first physical quantity obtained by filtering using the test filter, represents the first physical quantity obtained by filtering using the test filter, represents the norm of the first physical quantity obtained by filtering using the grid filter, Represents the filtering process of the test filter.

[0196] In an optional embodiment, the analytical vortex flux calculation module 12 is specifically used for:

[0197] The analytical vortex flux calculation formula is used to calculate the analytical vortex flux based on the target flow field velocity and the target vortex; the analytical vortex flux calculation formula is:

[0198] ;

[0199] in, To resolve the vorticity flux, , is the flow field velocity obtained by filtering with a grid filter using large eddy simulation, , is the flow field velocity obtained by filtering using the test filter, , is the vorticity obtained by filtering using the grid filter of large eddy simulation, , is the vorticity obtained by filtering using the test filter, Represents the filtering process of the test filter, and i and j represent different directions.

[0200] In an optional implementation, the first physical quantity calculation module 13 is specifically used to:

[0201] The first physical quantity is determined based on the target vorticity using a preset first physical quantity calculation formula; the preset first physical quantity calculation formula is:

[0202] , ;

[0203] in, represents the first physical quantity after filtering by the grid filter, , represents the vorticity obtained by filtering using a grid filter, Represents the first physical quantity after the test filter is filtered. , represents the vorticity obtained by filtering using the test filter, , is the distance vector, i and j represent different directions.

[0204] The vorticity transport equation is:

[0205] ;

[0206] in, is the vorticity obtained by filtering using the grid filter of large eddy simulation, is the flow field velocity obtained by filtering with a grid filter using large eddy simulation, is the eddy viscosity coefficient, t is the time, is the distance vector, is the filter width of the grid filter, represents the norm of the first physical quantity obtained by filtering using the grid filter, represents the first physical quantity after filtering by the grid filter, represents the kinematic viscosity coefficient, , Represents the vorticity obtained by filtering using a grid filter, and i and j represent different directions.

[0207] The flow field velocity calculation module 16 specifically uses a first preset formula and updates the stream function vector based on the vorticity obtained by filtering the grid filter using large eddy simulation at the next moment corresponding to the previous moment; the first preset formula is:

[0208] ;

[0209] in, is the stream function vector, is the distance vector, is the vorticity obtained by filtering with a grid filter using large eddy simulation, i and j represent different directions;

[0210] The velocity potential function is updated using the second preset formula and according to the flow field velocity obtained by filtering the grid filter using the large eddy simulation at the previous moment; the second preset formula is:

[0211] ;

[0212] in, is the velocity potential function, is the flow field velocity obtained by filtering the grid filter using large eddy simulation at the previous moment;

[0213] The flow field velocity obtained by filtering the grid filter using large eddy simulation at the next moment corresponding to the previous moment is calculated using a third preset formula based on the updated stream function vector and the velocity potential function; the third preset formula is:

[0214] ;

[0215] in, is the substitution symbol, is the stream function vector, is the distance vector, The flow field velocity at the next moment is obtained by filtering the grid filter using large eddy simulation;

[0216] The flow field velocity at the next moment obtained by filtering using the test filter is calculated based on the flow field velocity obtained by filtering using the grid filter of the large eddy simulation at the next moment.

[0217] It can be seen that the embodiment of the present application is based on the pseudo-eddy energy power conservation relationship of the flow structure whose scale is between the filtering width of the grid filter and the filtering width of the test filter. According to the local flow characteristics of the flow field, the eddy viscosity coefficient can be adaptively calculated, thereby accurately determining the vorticity and velocity of the flow field.

[0218] See also Figure 5 As shown, an embodiment of the present application discloses an electronic device 20, including a processor 21 and a memory 22; wherein the memory 22 is used to store a computer program; the processor 21 is used to execute the computer program, the vorticity and velocity method of large eddy simulation disclosed in the above embodiment.

[0219] For the specific process of the above-mentioned vorticity and velocity method of large eddy simulation, reference may be made to the corresponding contents disclosed in the aforementioned embodiments, which will not be repeated here.

[0220] Furthermore, the memory 22 as a carrier for storing resources may be a read-only memory, a random access memory, a magnetic disk or an optical disk, etc., and the storage method may be temporary storage or permanent storage.

[0221] In addition, the electronic device 20 also includes a power supply 23, a communication interface 24, an input / output interface 25 and a communication bus 26; wherein the power supply 23 is used to provide working voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and an external device, and the communication protocol it follows is any communication protocol that can be applied to the technical solution of the present application, and is not specifically limited here; the input / output interface 25 is used to obtain external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0222] Furthermore, an embodiment of the present application also discloses a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the vorticity and velocity method of large eddy simulation disclosed in the aforementioned embodiment.

[0223] For the specific process of the above-mentioned vorticity and velocity method of large eddy simulation, reference may be made to the corresponding contents disclosed in the aforementioned embodiments, which will not be repeated here.

[0224] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0225] The steps of the method or algorithm described in conjunction with the embodiments disclosed herein may be implemented directly using hardware, a software module executed by a processor, or a combination of the two. The software module may be placed in a random access memory (RAM), a memory, a read-only memory (ROM), an electrically programmable ROM, an electrically erasable programmable ROM, a register, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.

[0226] The above is a detailed introduction to the method, device, equipment and medium for determining the vorticity and velocity of a large eddy simulation provided by the present application. Specific examples are used in this article to illustrate the principles and implementation methods of the present application. The description of the above embodiments is only used to help understand the method of the present application and its core idea; at the same time, for general technical personnel in this field, according to the idea of ​​the present application, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as a limitation on the present application.

Claims

1. A method for determining vorticity and velocity in large eddy simulation, characterized in that: include: Obtaining a target flow field velocity at a previous moment and a target vorticity at a previous moment, wherein the target flow field velocity includes a flow field velocity obtained by filtering with a grid filter of large eddy simulation and a flow field velocity obtained by filtering with a test filter, and the target vorticity includes a vorticity obtained by filtering with a grid filter of large eddy simulation and a vorticity obtained by filtering with a test filter, and the test filter is a filter having a grid size larger than a grid size of the grid filter; Calculating an analytical vorticity flux based on the target flow field velocity and the target vorticity, wherein the analytical vorticity flux characterizes the contribution of a flow structure having a scale between a filter width of the grid filter and a filter width of the test filter to vorticity transport; Calculate a target first physical quantity based on the target vorticity, the target first physical quantity includes a first physical quantity obtained by filtering using the grid filter and a first physical quantity obtained by filtering using the test filter, wherein the first physical quantity is a symmetric tensor representing a spatial variation of a vorticity field; The eddy viscosity coefficient is calculated based on the analytical vortex flux and the target first physical quantity and using an eddy viscosity coefficient calculation formula, wherein the eddy viscosity coefficient calculation formula is established based on a pseudo-eddy energy power conservation relationship of a flow structure whose scale is between the filter width of the grid filter and the filter width of the test filter; A vorticity transport equation is closed based on the eddy viscosity coefficient, and a target vorticity at a next moment corresponding to the previous moment is determined based on the vorticity transport equation; Based on the flow field velocity obtained by filtering using a grid filter of large eddy simulation at the previous moment and the vorticity obtained by filtering using a grid filter of large eddy simulation at the next moment corresponding to the previous moment, the target flow field velocity at the next moment corresponding to the previous moment is calculated.

2. The method for determining vorticity and velocity of large eddy simulation according to claim 1, characterized in that: The eddy viscosity coefficient calculation formula is: ； in, is the eddy viscosity coefficient, To resolve the vorticity flux, , , represents the first physical quantity obtained by filtering using the grid filter, To test the filter width, is the filter width of the grid filter, represents the norm of the first physical quantity obtained by filtering using the test filter, represents the first physical quantity obtained by filtering using the test filter, represents the norm of the first physical quantity obtained by filtering using the grid filter, Represents the filter processing of the test filter.

3. The method for determining vorticity and velocity of large eddy simulation according to claim 1, characterized in that: When the preset flow field uniformity condition is met, the eddy viscosity coefficient calculation formula is: ； in, is the eddy viscosity coefficient, To resolve the vorticity flux, , , represents the first physical quantity obtained by filtering using the grid filter, is the filter width of the grid filter, represents the norm of the first physical quantity obtained by filtering using the test filter, represents the first physical quantity obtained by filtering using the test filter, represents the norm of the first physical quantity obtained by filtering using the grid filter, Represents the filtering process of the test filter.

4. The method for determining vorticity and velocity of large eddy simulation according to claim 1, characterized in that: The calculating of the analytical vorticity flux based on the target flow field velocity and the target vorticity comprises: The analytical vortex flux calculation formula is used to calculate the analytical vortex flux based on the target flow field velocity and the target vortex; the analytical vortex flux calculation formula is: ； in, To resolve the vorticity flux, , is the flow field velocity obtained by filtering with a grid filter using large eddy simulation, , is the flow field velocity obtained by filtering using the test filter, , is the vorticity obtained by filtering using the grid filter of large eddy simulation, , is the vorticity obtained by filtering using the test filter, Represents the filtering process of the test filter, and i and j represent different directions.

5. The method for determining vorticity and velocity of large eddy simulation according to claim 1, characterized in that: The calculating of the target first physical quantity based on the target vorticity comprises: The first physical quantity is determined based on the target vorticity using a preset first physical quantity calculation formula; the preset first physical quantity calculation formula is: 、 ; in, represents the first physical quantity after filtering by the grid filter, , represents the vorticity obtained by filtering using a grid filter, Represents the first physical quantity after the test filter is filtered. , represents the vorticity obtained by filtering using the test filter, , is the distance vector, i and j represent different directions.

6. The method for determining vorticity and velocity in large eddy simulation according to any one of claims 1 to 5, characterized in that: The vorticity transport equation is: ； in, is the vorticity obtained by filtering using the grid filter of large eddy simulation, is the flow field velocity obtained by filtering with a grid filter using large eddy simulation, is the eddy viscosity coefficient, t is the time, is the distance vector, is the filter width of the grid filter, represents the norm of the first physical quantity obtained by filtering using the grid filter, represents the first physical quantity after filtering by the grid filter, represents the kinematic viscosity coefficient, , Represents the vorticity obtained by filtering using a grid filter, and i and j represent different directions.

7. The method for determining vorticity and velocity in large eddy simulation according to claim 1, characterized in that: The method of calculating the target flow field velocity at the next moment corresponding to the previous moment based on the flow field velocity obtained by filtering using the grid filter of large eddy simulation at the previous moment and the vorticity obtained by filtering using the grid filter of large eddy simulation at the next moment corresponding to the previous moment comprises: The stream function vector is updated by using a first preset formula and based on the vorticity obtained by filtering the grid filter using large eddy simulation at the next moment corresponding to the previous moment; the first preset formula is: ； in, is the stream function vector, is the distance vector, is the vorticity obtained by filtering with a grid filter using large eddy simulation, i and j represent different directions; The velocity potential function is updated using the second preset formula and according to the flow field velocity obtained by filtering the grid filter using the large eddy simulation at the previous moment; the second preset formula is: ； in, is the velocity potential function, is the flow field velocity obtained by filtering the grid filter using large eddy simulation at the previous moment; The flow field velocity obtained by filtering the grid filter using large eddy simulation at the next moment corresponding to the previous moment is calculated using a third preset formula based on the updated stream function vector and the velocity potential function; the third preset formula is: ； in, is the substitution symbol, is the stream function vector, is the distance vector, The flow field velocity at the next moment is obtained by filtering the grid filter using large eddy simulation; The flow field velocity at the next moment obtained by filtering using the test filter is calculated based on the flow field velocity obtained by filtering using the grid filter of the large eddy simulation at the next moment.

8. A device for determining vorticity and velocity in large eddy simulation, characterized in that: include: A velocity and vorticity acquisition module, used to acquire a target flow field velocity and a target vorticity at a previous moment, wherein the target flow field velocity includes a flow field velocity obtained by filtering a grid filter of large eddy simulation and a flow field velocity obtained by filtering a test filter, and the target vorticity includes a vorticity obtained by filtering a grid filter of large eddy simulation and a vorticity obtained by filtering a test filter, and the test filter is a filter having a grid size larger than a grid size of the grid filter; An analytical vorticity flux calculation module, used for calculating an analytical vorticity flux based on the target flow field velocity and the target vorticity, wherein the analytical vorticity flux characterizes the contribution of a flow structure having a scale between a filter width of the grid filter and a filter width of the test filter to vorticity transport; A first physical quantity calculation module, used for calculating a target first physical quantity based on the target vorticity, wherein the target first physical quantity includes a first physical quantity obtained by filtering using the grid filter and a first physical quantity obtained by filtering using the test filter, wherein the first physical quantity is a symmetric tensor representing a spatial variation of a vorticity field; An eddy viscosity coefficient calculation module, used for calculating the eddy viscosity coefficient based on the analytical vortex flux, the target first physical quantity and using an eddy viscosity coefficient calculation formula, wherein the eddy viscosity coefficient calculation formula is established based on a pseudo-eddy energy power conservation relationship of a flow structure whose scale is between the filter width of the grid filter and the filter width of the test filter; A target vorticity calculation module, used for closing the vorticity transport equation based on the eddy viscosity coefficient, and determining the target vorticity at the next moment corresponding to the previous moment based on the vorticity transport equation; The flow field velocity calculation module is used to calculate the target flow field velocity at the next moment corresponding to the previous moment based on the flow field velocity obtained by filtering using a grid filter using large eddy simulation at the previous moment and the vorticity obtained by filtering using a grid filter using large eddy simulation at the next moment corresponding to the previous moment.

9. An electronic device, characterized in that: comprising a memory and a processor, wherein: The memory is used to store the computer program; The processor is used to execute the computer program to implement the method for determining vorticity and velocity of large eddy simulation according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: Used to store a computer program, wherein when the computer program is executed by a processor, the method for determining vorticity and velocity in large eddy simulation according to any one of claims 1 to 7 is implemented.

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