CN115563898A - Solid wall boundary numerical simulation method based on non-body-attached grid and related equipment - Google Patents

Solid wall boundary numerical simulation method based on non-body-attached grid and related equipment Download PDF

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CN115563898A
CN115563898A CN202211254384.0A CN202211254384A CN115563898A CN 115563898 A CN115563898 A CN 115563898A CN 202211254384 A CN202211254384 A CN 202211254384A CN 115563898 A CN115563898 A CN 115563898A
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武从海
王益民
刘旭亮
张树海
韩帅斌
罗勇
李虎
马瑞轩
王笑佩
袁思齐
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Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
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Abstract

The invention is suitable for the technical field of computational fluid mechanics boundary processing, and provides a fixed wall boundary numerical simulation method based on a non-body-attached grid and related equipment, wherein the method comprises the following steps: acquiring flow field values of a plurality of grid nodes of a non-skin grid adjacent to a solid wall boundary, wherein the grid nodes comprise first-layer grid nodes near the boundary, and the flow field values comprise first flow field values of the first-layer grid nodes; reconstructing flow field values based on a plurality of grid nodes to obtain a first boundary value flux; setting a solid wall boundary condition, combining the solid wall boundary condition with flow field values of a plurality of grid nodes, and correcting a first flow field value of a first layer of grid nodes to obtain a second flow field value of the first layer of grid nodes; and reconstructing based on the second flow field value to obtain a second boundary numerical flux, obtaining a third boundary numerical flux according to the first boundary numerical flux and the second boundary numerical flux, and simulating a solid wall boundary of the non-skin mesh by using the third boundary numerical flux. The solid wall boundary of the non-skin grid can be simulated better and more accurately.

Description

Solid wall boundary numerical simulation method based on non-body-attached grid and related equipment
Technical Field
The invention relates to the technical field of computational fluid mechanics boundary processing, in particular to a method, a device, computer equipment and a computer readable storage medium for simulating a fixed wall boundary numerical value based on a non-body-attached grid.
Background
In numerical simulation of complex flow, two processing methods, namely a conformal grid and a non-conformal grid, exist. Although most existing commercial software employs a mesh of the skin, non-skin meshes are of increasing interest due to the relative simplicity of mesh generation. For non-conformal grids, a key problem is the processing of the boundary condition of the fixed wall, and the most common processing method at present is the immersion boundary method based on virtual points, which sets virtual grid nodes at the boundary or inside the fixed wall, and the values of the virtual grid nodes are determined by the boundary condition and the control equation together. However, for the vicinity of the boundary where the solid wall boundary is in the shape of an acute angle, a thin plate, or the like, the virtual grid node may coincide with the actual grid node, so that the setting of the virtual grid node cannot better simulate the boundary, or the virtual grid node needs to be set according to different boundaries, which may cause difficulty in processing the program.
Disclosure of Invention
The invention aims to provide a solid wall boundary numerical simulation method based on a non-skin grid, which can better simulate the solid wall boundary of the non-skin grid under the condition of not setting virtual grid nodes and avoid the problems of node setting superposition, program processing difficulty and the like caused by processing the solid wall boundary of the non-skin grid by setting the virtual grid nodes in the prior art.
In a first aspect, an embodiment of the present invention provides a fixed-wall boundary numerical simulation method based on a non-conformal mesh, including:
s1, obtaining flow field values of a plurality of grid nodes of a non-skin grid adjacent to a solid wall boundary, wherein the grid nodes comprise first-layer grid nodes near the boundary, and the flow field values comprise first flow field values of the first-layer grid nodes;
s2, reconstructing flow field values based on the grid nodes to obtain a first boundary value flux;
s3, setting a solid wall boundary condition, combining the solid wall boundary condition with the flow field values of the grid nodes, and correcting the first flow field value of the first layer of grid nodes to obtain a second flow field value of the first layer of grid nodes;
s4, reconstructing based on the second flow field value to obtain a second boundary numerical flux, obtaining a third boundary numerical flux according to the first boundary numerical flux and the second boundary numerical flux, and simulating a solid wall boundary of the non-skin grid by using the third boundary numerical flux.
Further, the reconstructing the flow field values based on the plurality of grid nodes to obtain the first boundary value flux includes:
and carrying out eccentric reconstruction on the flow field values of the grid nodes to obtain the first boundary value flux.
Further, the step of setting a solid wall boundary condition, combining the solid wall boundary condition with the flow field values of the plurality of grid nodes, and correcting the first flow field value of the first layer of grid nodes to obtain a second flow field value of the first layer of grid nodes includes:
determining the corresponding first-layer grid node on the fixed wall boundary
Figure 100002_DEST_PATH_IMAGE001
Boundary node of (2)
Figure 218660DEST_PATH_IMAGE002
So that the first layer mesh node
Figure 871359DEST_PATH_IMAGE001
And said border node
Figure 647685DEST_PATH_IMAGE002
The connecting line direction of the fixed wall is the external normal direction of the fixed wall boundary;
obtaining nodes near the boundary
Figure 335018DEST_PATH_IMAGE002
Including the first-layer mesh nodes
Figure 100002_DEST_PATH_IMAGE003
First flow field value of
Figure 53444DEST_PATH_IMAGE004
；
Computing the boundary nodes by extrapolation based on the original flow field values of the plurality of grid nodes
Figure 68805DEST_PATH_IMAGE002
Original flow field value of
Figure 100002_DEST_PATH_IMAGE005
And its first and second boundary normal derivatives
Figure 773456DEST_PATH_IMAGE006
、
Figure 100002_DEST_PATH_IMAGE007
；
Connecting the boundary node
Figure 705508DEST_PATH_IMAGE002
Original flow field value of
Figure 939044DEST_PATH_IMAGE005
And first and second derivatives
Figure 441700DEST_PATH_IMAGE006
、
Figure 418884DEST_PATH_IMAGE007
Rotating to the external normal direction of the fixed wall boundary to obtain the boundary node
Figure 205443DEST_PATH_IMAGE002
Value of the rotating flow field
Figure 875459DEST_PATH_IMAGE008
And its first and second normal derivatives
Figure DEST_PATH_IMAGE009
、
Figure 865411DEST_PATH_IMAGE010
；
For the boundary node
Figure 646286DEST_PATH_IMAGE002
Value of the rotating flow field
Figure 287351DEST_PATH_IMAGE008
And its first and second normal derivatives
Figure 862689DEST_PATH_IMAGE009
、
Figure 198993DEST_PATH_IMAGE010
Carrying out feature projection to obtain boundary nodes
Figure 393345DEST_PATH_IMAGE002
Projected value of the rotating flow field
Figure DEST_PATH_IMAGE011
And its first and second normal derivatives
Figure 29862DEST_PATH_IMAGE012
、
Figure DEST_PATH_IMAGE013
；
The boundary node on the fixed wall boundary
Figure 431894DEST_PATH_IMAGE014
Is set to zero, in conjunction with the boundary node
Figure 396439DEST_PATH_IMAGE002
Projected value of the rotating flow field
Figure 253536DEST_PATH_IMAGE011
Adjusting the value of its rotating flow field
Figure DEST_PATH_IMAGE015
And fixing the boundary nodes on the wall boundary
Figure 134773DEST_PATH_IMAGE002
Is arranged according to a centripetal force formula and is combined with the boundary node
Figure 317493DEST_PATH_IMAGE002
First order normal derivative of the projected value of the rotating flow field
Figure 362809DEST_PATH_IMAGE016
Adjusting the boundary node
Figure 164543DEST_PATH_IMAGE002
First order normal derivative of the rotating flow field value
Figure DEST_PATH_IMAGE017
；
Figure 900287DEST_PATH_IMAGE018
Adjusted border node
Figure 253908DEST_PATH_IMAGE002
Value of the rotating flow field of
Figure 927466DEST_PATH_IMAGE008
Performing Taylor series expansion along the external normal direction of the fixed wall boundary to obtain the first layer of grid nodes
Figure 391945DEST_PATH_IMAGE001
Value of the rotating flow field of
Figure DEST_PATH_IMAGE019
；
Passing through the first layer mesh nodes
Figure 982196DEST_PATH_IMAGE001
Value of the rotating flow field
Figure 506718DEST_PATH_IMAGE019
Obtaining a second flow field value of the first layer of grid nodes
Figure 526626DEST_PATH_IMAGE020
Further, the boundary node after adjustment
Figure 935742DEST_PATH_IMAGE002
Value of the rotating flow field
Figure 724707DEST_PATH_IMAGE008
Carrying out Taylor series expansion along the external normal direction of the solid wall boundary to obtain the first layer of grid nodesPValue of the rotating flow field
Figure DEST_PATH_IMAGE021
Comprises the following steps:
computing the first-tier mesh nodes
Figure 810343DEST_PATH_IMAGE001
And said border node
Figure 583127DEST_PATH_IMAGE002
Length betweenh；
Based on the boundary node
Figure 264775DEST_PATH_IMAGE002
Value of the rotating flow field of
Figure 173825DEST_PATH_IMAGE008
The first normal derivative
Figure 40150DEST_PATH_IMAGE017
The second order normal derivative
Figure 159285DEST_PATH_IMAGE022
And said lengthhComputing the first-tier mesh nodesPValue of the rotating flow field of
Figure 769258DEST_PATH_IMAGE019
。
Further, the passing of the first-layer mesh nodesPValue of the rotating flow field
Figure 408181DEST_PATH_IMAGE019
Obtaining the first layer grid node
Figure 445407DEST_PATH_IMAGE001
Second flow field value of
Figure 927204DEST_PATH_IMAGE020
The method comprises the following steps:
connecting the first layer mesh nodesPValue of the rotating flow field
Figure 199922DEST_PATH_IMAGE019
Rotating the outer normal direction of the fixed wall boundary to the original direction to obtain the corrected first layer of grid nodes
Figure 83564DEST_PATH_IMAGE001
Second flow field value of
Figure 432637DEST_PATH_IMAGE020
。
Further, the reconstructing based on the second flow field value to obtain a second boundary numerical flux, and obtaining a third boundary numerical flux according to the first boundary numerical flux and the second boundary numerical flux includes:
based on the first layer mesh node
Figure 136151DEST_PATH_IMAGE001
Corrected second flow field value
Figure 353506DEST_PATH_IMAGE020
Carrying out eccentric reconstruction to obtain the flux of the second boundary numerical value;
obtaining the first layer of grid nodes
Figure 950709DEST_PATH_IMAGE001
First flow field value before correction
Figure 595317DEST_PATH_IMAGE020
A feature matrix of (a);
and calculating to obtain the third boundary value flux based on the first boundary value flux, the second boundary value flux and the feature matrix.
Further, the step of simulating the fixed-wall boundary of the non-conformal mesh by using the third boundary numerical flux includes:
and updating the flow field value of the grid node according to the flux of the third boundary value, and simulating the fixed wall boundary of the non-skin grid based on the updated flow field value of the grid node.
In a second aspect, an embodiment of the present invention provides a solid-wall boundary numerical simulation apparatus based on a non-conformal mesh, including:
the device comprises an acquisition module, a data processing module and a data processing module, wherein the acquisition module is used for acquiring flow field values of a plurality of grid nodes of a non-skin grid adjacent to a solid wall boundary, the grid nodes comprise first-layer grid nodes near the boundary, and the flow field values comprise first flow field values of the first-layer grid nodes;
the reconstruction module is used for reconstructing flow field values based on the grid nodes to obtain a first boundary value flux;
the correction module is used for setting a solid wall boundary condition, combining the solid wall boundary condition with the flow field values of the grid nodes, correcting the first flow field value of the first layer of grid nodes, and obtaining a second flow field value of the first layer of grid nodes;
and the simulation module is used for reconstructing based on the second flow field value to obtain a second boundary numerical flux, obtaining a third boundary numerical flux according to the first boundary numerical flux and the second boundary numerical flux, and simulating the solid-wall boundary of the non-skin grid by using the third boundary numerical flux.
In a third aspect, an embodiment of the present invention provides a computer device, including: the device comprises a memory, a processor and a computer program which is stored on the memory and can run on the processor, wherein the processor executes the computer program to realize the steps in the non-skin-mesh-based solid wall boundary numerical simulation method.
In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the computer program implements the steps in the non-skin mesh-based fixed wall boundary numerical simulation method.
Compared with the prior art, the embodiment of the invention mainly has the following beneficial effects: the method comprises the steps of reconstructing flow field values of a plurality of grid nodes based on non-close grid solid wall boundaries to obtain a first boundary value flux, and correcting the first flow field value of a first layer of grid nodes near the boundaries by combining solid wall boundary conditions and the flow field values of the grid nodes to obtain a corrected second flow field value; and reconstructing based on the corrected second flow field value to obtain a second boundary numerical flux, obtaining a third boundary numerical flux according to the first boundary numerical flux and the second boundary numerical flux, and finally simulating a fixed wall boundary of the non-skin grid by using the third boundary numerical flux so as to introduce boundary information into flow field numerical simulation of the non-skin grid.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments of the present invention or in the description of the prior art will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of one embodiment of a non-skin mesh-based solid wall boundary numerical simulation method of the present invention;
FIG. 2 is a schematic structural diagram of one embodiment of a one-dimensional mesh node near a non-skin mesh solid wall boundary of the present invention;
FIG. 3 is a schematic structural diagram of one embodiment of a two-dimensional mesh node near a non-conformal mesh fixed-wall boundary of the present invention;
FIG. 4 is a schematic structural diagram of an embodiment of a non-conformal mesh-based solid-wall boundary numerical simulation apparatus according to the present invention;
fig. 5 is a schematic diagram of a basic structure of a computer device according to the present invention.
In fig. 4: 401. an acquisition module 402, a reconstruction module 403, a correction module 404 and a simulation module;
in fig. 5: 500. computer device, 501, memory, 502, processor, 503, network interface.
Detailed Description
The following description provides many different embodiments, or examples, for implementing different features of the invention. The particular examples set forth below are illustrative only and are not intended to be limiting.
In order to make the technical solutions better understood by those skilled in the art, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.
As shown in fig. 1, fig. 1 is a flowchart of an embodiment of a non-skin-mesh-based fixed wall boundary numerical simulation method according to the present invention, where the non-skin-mesh-based fixed wall boundary numerical simulation method includes the following steps:
s1, obtaining flow field values of a plurality of grid nodes of a non-skin grid adjacent to a solid wall boundary, wherein the grid nodes comprise first-layer grid nodes near the boundary, and the flow field values comprise first flow field values of the first-layer grid nodes;
and S2, reconstructing based on the flow field values of the grid nodes to obtain a first boundary value flux.
In the embodiment of the invention, the complex fluid flow is simulated by the non-body grid, and the fluid flow control equation (or flow field control equation) can be used
Figure DEST_PATH_IMAGE023
The flow field value of the grid node in the non-body-fitted grid can be obtained by solving a flow field control equation; whereinWThe flow field variable is represented by a variable,
Figure DEST_PATH_IMAGE025
represents
Figure 458231DEST_PATH_IMAGE026
The derivative with respect to time is that of,
Figure DEST_PATH_IMAGE027
represent
Figure 603910DEST_PATH_IMAGE026
The derivative to space.
If the fluid flows in one-dimensional inviscid flow, the flow field variable thereof
Figure 462145DEST_PATH_IMAGE028
I.e. byWIs a vector consisting of density, velocity and pressure,
Figure DEST_PATH_IMAGE029
is a feature matrix of and
Figure DEST_PATH_IMAGE031
(ii) a If the fluid flows in two dimensions without viscosity, the flow field variable therein
Figure 418600DEST_PATH_IMAGE032
I.e. byWIs prepared from the components of density,
Figure DEST_PATH_IMAGE033
The speed of the rotation,
Figure 752498DEST_PATH_IMAGE034
Vector formed by velocity and pressure.
The grid nodes are composed of nodes close to the non-body grid fixed wall boundary. Specifically, if there is one-dimensional inviscid flow, the mesh nodes near the solid wall boundary of the non-skin mesh are shown in fig. 2, wherein
Figure DEST_PATH_IMAGE035
Are the nodes of the mesh that are close to the boundary,
Figure 452601DEST_PATH_IMAGE036
being the first layer of mesh nodes near the boundary,
Figure DEST_PATH_IMAGE037
are boundary nodes and do not belong to nodes in non-body meshes. The flow field value corresponding to the above-mentioned grid node is
Figure 555555DEST_PATH_IMAGE038
，
Figure DEST_PATH_IMAGE039
A first flow field value for said first layer of mesh nodes; then reconstructing the flow field values to obtain a first boundary numerical flux, and specifically performing eccentric reconstruction on the flow field values of a plurality of grid nodes to obtain the first boundary numerical flux; in the field of computational fluid mechanics, numerical flux generally refers to flow field variablesWThe inflow (outflow) amount of the unit interface (i.e. the spatial variation amount of density, velocity and pressure in the flow field); further, the numerical derivative can be calculated by dividing the difference in numerical flux across the cell interface by the grid spacing.
The process of obtaining the numerical flux from the flow field value of the grid node is called reconstruction, and if the second-order method is:
Figure 948490DEST_PATH_IMAGE040
wherein, the first and the second end of the pipe are connected with each other,fflow field values representing nodes of the gridW，
Figure DEST_PATH_IMAGE041
Representing the numerical flux between the nodes of the grid
Figure 379471DEST_PATH_IMAGE042
(ii) a In the present invention, however, the nodes on the boundary are
Figure DEST_PATH_IMAGE043
No flow field value exists, so that boundary nodes
Figure 878672DEST_PATH_IMAGE043
Flux of nearby boundary values
Figure 445920DEST_PATH_IMAGE044
Cannot adopt the formula, but can pass through the mesh node
Figure DEST_PATH_IMAGE045
，
Figure 744177DEST_PATH_IMAGE046
The flow field value is obtained by an eccentric reconstruction method, and the calculation formula is as follows:
Figure DEST_PATH_IMAGE047
if the two-dimensional non-adhesive flow exists, the grid nodes near the solid wall boundary of the non-attached grid are shown in FIG. 3, wherein the circular arc line is the boundary, the solid nodes are the grid nodes, and the thickened grid nodes are the grid nodes
Figure 787088DEST_PATH_IMAGE001
Is the first layer grid node closest to the boundary, and the first flow field value of the first layer grid node is
Figure 688048DEST_PATH_IMAGE048
；
Figure 985168DEST_PATH_IMAGE002
As nodes on the boundary, in the present invention boundary nodes
Figure 313382DEST_PATH_IMAGE002
For nodes not belonging to non-tessellated meshes, only boundary nodes are obtained
Figure 187797DEST_PATH_IMAGE002
Is 0. Near-boundary first-layer grid node
Figure 751502DEST_PATH_IMAGE001
In that
Figure 27763DEST_PATH_IMAGE033
First boundary value flux in axial direction (horizontal direction in fig. 3)
Figure 402243DEST_PATH_IMAGE042
By using
Figure DEST_PATH_IMAGE049
Meaning that it is also obtained by means of the above-described off-center reconstruction, selecting a number of grid nodes, e.g. grid nodes, in the vicinity of the same grid lineP、NEtc. flow field value
Figure 295113DEST_PATH_IMAGE004
、
Figure 396930DEST_PATH_IMAGE050
And (4) calculating. The flow field values of a plurality of grid nodes nearby on the same grid line of the first layer of grid nodes nearby the boundary are adopted, the numerical flux nearby the boundary nodes is calculated in an eccentric reconstruction mode, and the first boundary numerical flux which is accurate can be obtained.
And S3, setting a solid wall boundary condition, combining the solid wall boundary condition with the flow field values of the grid nodes, and correcting the first flow field value of the first layer of grid nodes to obtain a second flow field value of the first layer of grid nodes.
Further, the flow field values of the plurality of grid nodes include an original flow field value, and the step S3 specifically includes:
determining the corresponding first layer grid node on the fixed wall boundary
Figure 793276DEST_PATH_IMAGE001
Boundary node of
Figure 197713DEST_PATH_IMAGE002
So that the first layer mesh node
Figure 187666DEST_PATH_IMAGE001
And said border node
Figure 968540DEST_PATH_IMAGE002
The connecting line direction of the fixed wall is the external normal direction of the fixed wall boundary;
obtaining a node close to the boundary
Figure 344026DEST_PATH_IMAGE002
A plurality ofOriginal flow field values of mesh nodes, including the first layer of mesh nodes
Figure 919364DEST_PATH_IMAGE001
First flow field value of
Figure 521247DEST_PATH_IMAGE004
；
Computing the boundary nodes by extrapolation based on the original flow field values of the plurality of grid nodes
Figure 715599DEST_PATH_IMAGE002
Original flow field value of
Figure 86537DEST_PATH_IMAGE005
And its first and second boundary normal derivatives
Figure 832776DEST_PATH_IMAGE006
、
Figure 46589DEST_PATH_IMAGE007
；
Connecting the boundary node
Figure 903687DEST_PATH_IMAGE014
Original flow field value of
Figure 4498DEST_PATH_IMAGE005
And first and second derivatives
Figure DEST_PATH_IMAGE051
Rotating to the external normal direction of the fixed wall boundary to obtain the boundary node
Figure 718376DEST_PATH_IMAGE002
Value of the rotating flow field
Figure 888326DEST_PATH_IMAGE008
And its normal first and second derivatives
Figure 814694DEST_PATH_IMAGE009
、
Figure 894645DEST_PATH_IMAGE010
。
For the boundary node
Figure 858053DEST_PATH_IMAGE002
Value of the rotating flow field of
Figure 656245DEST_PATH_IMAGE008
And its first normal derivative
Figure 510937DEST_PATH_IMAGE017
Carrying out feature projection to obtain boundary nodes
Figure 179816DEST_PATH_IMAGE002
Projected value of the rotating flow field
Figure 704338DEST_PATH_IMAGE011
And its first normal derivative
Figure 458668DEST_PATH_IMAGE016
；
The boundary node on the fixed wall boundary
Figure 867783DEST_PATH_IMAGE002
Is set to zero, in conjunction with the boundary node
Figure 656748DEST_PATH_IMAGE002
Projected value of the rotating flow field
Figure 7964DEST_PATH_IMAGE011
Adjusting the value of its rotating flow field
Figure 249589DEST_PATH_IMAGE015
And connecting the boundary nodes on the fixed wall boundary
Figure 790292DEST_PATH_IMAGE002
Normal pressure ofThe derivatives are arranged according to a centripetal force formula, in combination with said boundary nodes
Figure 840287DEST_PATH_IMAGE002
First order normal derivative of the projected value of the rotating flow field
Figure 972191DEST_PATH_IMAGE016
Adjusting the boundary node
Figure 701113DEST_PATH_IMAGE002
First order normal derivative of the rotating flow field value
Figure 170141DEST_PATH_IMAGE017
；
The adjusted boundary node
Figure 199276DEST_PATH_IMAGE002
Value of the rotating flow field of
Figure 377448DEST_PATH_IMAGE008
Carrying out Taylor series expansion along the external normal direction of the solid wall boundary to obtain the first layer of grid nodes
Figure 328086DEST_PATH_IMAGE001
Value of the rotating flow field
Figure 741750DEST_PATH_IMAGE019
；
Passing through the first layer mesh nodes
Figure 15606DEST_PATH_IMAGE001
Value of the rotating flow field
Figure 223733DEST_PATH_IMAGE019
Obtaining the first layer grid nodesPSecond flow field value of
Figure 68192DEST_PATH_IMAGE020
。
In the present example, there is no adhesion for two dimensionsFlow field, first layer of grid nodes near the above boundaryPCorresponding boundary node
Figure 19968DEST_PATH_IMAGE002
From the boundary geometry information andPdetermining the position of the point to make the first layer of grid nodesPAnd the above boundary node
Figure 492537DEST_PATH_IMAGE002
Direction of connecting line (in)
Figure 261779DEST_PATH_IMAGE052
See FIG. 3) is the outer normal of the above-mentioned solid-wall boundary, i.e. the boundary node
Figure 718168DEST_PATH_IMAGE002
Is the intersection of the outer normal and the solid wall boundary. And then combining the fixed wall boundary conditions to grid nodesPThe value of (c) is corrected. Specifically, the closest border node may be obtained
Figure 942476DEST_PATH_IMAGE002
A plurality of grid nodes (including nodes) in the vicinity ofPAndPsurrounding mesh nodes) of the original flow field value
Figure 410498DEST_PATH_IMAGE026
(including first tier mesh nodes
Figure 226007DEST_PATH_IMAGE001
First flow field value of
Figure 294326DEST_PATH_IMAGE004
) Based on
Figure 853483DEST_PATH_IMAGE026
Boundary node acquisition by extrapolation
Figure 35066DEST_PATH_IMAGE002
Flow field value
Figure 631264DEST_PATH_IMAGE005
And the first and second normal derivatives thereof, and rotating to the outer normal direction of the fixed wall boundary to obtain boundary nodes
Figure 62245DEST_PATH_IMAGE002
Value of rotating flow field
Figure 284148DEST_PATH_IMAGE008
And its first and second normal derivatives
Figure 585816DEST_PATH_IMAGE017
、
Figure 477549DEST_PATH_IMAGE022
Then to
Figure 271192DEST_PATH_IMAGE008
、
Figure 172152DEST_PATH_IMAGE017
Performing characteristic projection to obtain projection value
Figure 62748DEST_PATH_IMAGE011
And its first and second normal derivatives
Figure 515595DEST_PATH_IMAGE016
、
Figure DEST_PATH_IMAGE053
(ii) a Wherein the projection matrixLAs mesh nodes
Figure 62114DEST_PATH_IMAGE001
Original flow field value of
Figure 235606DEST_PATH_IMAGE004
Rotate to the direction outside the boundary
Figure 433238DEST_PATH_IMAGE054
And left feature matrices for feature projection, e.g. for the aboveRotation variable of any point in two-dimensional flow field
Figure 401194DEST_PATH_IMAGE056
Wherein
Figure DEST_PATH_IMAGE057
，
Figure 435009DEST_PATH_IMAGE058
Respectively a normal direction velocity and a tangential direction velocity,
Figure DEST_PATH_IMAGE059
if the velocity of sound is sound, the corresponding left and right feature matrices are respectively
Figure DEST_PATH_IMAGE061
，
Figure DEST_PATH_IMAGE063
And is and
Figure 876441DEST_PATH_IMAGE064
is a unit matrix; recording boundary nodes
Figure 148154DEST_PATH_IMAGE002
Value of the rotating flow field
Figure 818169DEST_PATH_IMAGE066
Rotation of the projected value
Figure 401598DEST_PATH_IMAGE068
Combining the boundary condition and the projection value
Figure 307106DEST_PATH_IMAGE011
Can be paired with
Figure 823538DEST_PATH_IMAGE008
Adjusting and correcting, and specifically calculating by the following equation system:
Figure DEST_PATH_IMAGE069
in the system of equations for convenience
Figure 539821DEST_PATH_IMAGE070
And
Figure DEST_PATH_IMAGE071
all are provided with
Figure 797496DEST_PATH_IMAGE002
(same below), the first line of the equation set is defined by the above-mentioned wall-bounding boundary condition, i.e., the bounding wall normal velocity
Figure 382061DEST_PATH_IMAGE072
The value obtained is 0, and the value obtained is,
Figure DEST_PATH_IMAGE073
is a left feature matrixLTo (1) aiGo to the firstjElements of the column, and then the adjusted
Figure 628365DEST_PATH_IMAGE008
Performing Taylor series expansion along the external normal direction of the solid wall boundary to obtain the first layer of grid nodes
Figure 640184DEST_PATH_IMAGE001
Value of the rotating flow field
Figure 588417DEST_PATH_IMAGE019
。
Further, after adjustment
Figure 445515DEST_PATH_IMAGE008
Calculating the boundary nodes before Taylor series expansion along the external normal direction of the solid wall boundary
Figure 670960DEST_PATH_IMAGE002
Value of rotating flow field
Figure 729046DEST_PATH_IMAGE008
First order normal derivative of
Figure 305520DEST_PATH_IMAGE017
(ii) a And then based on the above rotating flow field value
Figure 700730DEST_PATH_IMAGE008
First and second normal derivatives
Figure 905315DEST_PATH_IMAGE017
，
Figure 524515DEST_PATH_IMAGE022
Further modifying first-level mesh nodes
Figure 198073DEST_PATH_IMAGE001
Value of the rotating flow field
Figure 396973DEST_PATH_IMAGE019
. Specifically, the above-mentioned boundary node
Figure 331431DEST_PATH_IMAGE002
First order normal derivative of rotating flow field value
Figure DEST_PATH_IMAGE075
Can be obtained by solving the following equation system
Figure 777325DEST_PATH_IMAGE076
Formula of centripetal force of first line of equation set by rotary motion
Figure DEST_PATH_IMAGE077
(pressure gradient equals centripetal force) wherein
Figure 938179DEST_PATH_IMAGE078
Is a boundary wall surface
Figure 206349DEST_PATH_IMAGE002
Curvature of pointA radius. The right end term in the last three rows is
Figure 385527DEST_PATH_IMAGE014
Projection value of point rotation
Figure 346529DEST_PATH_IMAGE016
The last three elements of (a).
The nodes of the first layer of grid can be obtained by correction through Taylor series expansion
Figure 729100DEST_PATH_IMAGE001
Value of the rotating flow field
Figure 800961DEST_PATH_IMAGE019
：
Figure DEST_PATH_IMAGE079
Wherein the content of the first and second substances,has a mesh node
Figure 100225DEST_PATH_IMAGE001
And boundary nodes
Figure 966550DEST_PATH_IMAGE014
The length in between. By aligning boundary nodes
Figure 101996DEST_PATH_IMAGE014
The extrapolated flow field value and the first-order second-order derivative thereof rotate to be better combined with the boundary condition, and the flow field value is adjusted after feature projection, so that the first flow field value of the first-layer grid node can be better corrected, and the corrected first-layer grid node can be more accurately obtained
Figure 180810DEST_PATH_IMAGE001
In particular the first layer of mesh nodes, of the first layer of mesh nodesPValue of the rotating flow field
Figure 209946DEST_PATH_IMAGE019
Rotating from the outer normal of the fixed wall boundary to the original direction to obtain the corrected first layer of grid nodes
Figure 371806DEST_PATH_IMAGE001
Second flow field value of
Figure 119182DEST_PATH_IMAGE020
。
S4, reconstructing based on the second flow field value to obtain a second boundary numerical flux, obtaining a third boundary numerical flux according to the first boundary numerical flux and the second boundary numerical flux, and simulating a solid wall boundary of the non-skin grid by using the third boundary numerical flux.
Further, the step S4 specifically includes:
based on the first layer mesh node
Figure 1688DEST_PATH_IMAGE001
Corrected second flow field value
Figure 760696DEST_PATH_IMAGE020
Carrying out eccentric reconstruction to obtain the flux of the second boundary numerical value;
obtaining the first layer grid node
Figure 234403DEST_PATH_IMAGE001
First flow field value before correction
Figure 328130DEST_PATH_IMAGE004
A feature matrix of (a);
and calculating to obtain the third boundary value flux based on the first boundary value flux, the second boundary value flux and the feature matrix.
In the embodiment of the invention, the first layer of grid nodes are firstly put into operationPValue of the rotating flow field
Figure 279905DEST_PATH_IMAGE019
The external normal direction of the fixed wall boundary is rotated to the original direction to obtain the grid node
Figure 752475DEST_PATH_IMAGE001
Corrected second flow field value
Figure 6870DEST_PATH_IMAGE020
(ii) a Then based on the first layer of grid nodes
Figure 463259DEST_PATH_IMAGE001
Corrected second flow field value
Figure 343359DEST_PATH_IMAGE020
And other grid node flow field values on the same grid line nearby, e.g. grid node in fig. 3N、MPerforming an eccentric reconstruction to obtain the second boundary numerical flux
Figure 670435DEST_PATH_IMAGE080
Specifically, the following second order reconstruction may be used:
Figure DEST_PATH_IMAGE081
the following third order reconstruction may also be employed:
Figure 892469DEST_PATH_IMAGE082
further obtaining the first layer grid node
Figure 836154DEST_PATH_IMAGE001
Flow field value before correction
Figure 598574DEST_PATH_IMAGE004
Left feature matrix ofLFirst row of
Figure DEST_PATH_IMAGE083
Right feature matrixRFirst column of (1)
Figure 967107DEST_PATH_IMAGE084
The net isGrid node
Figure 828884DEST_PATH_IMAGE001
Flow field value before correction (i.e. original flow field value)
Figure 728707DEST_PATH_IMAGE004
The feature matrix of the feature projection is the same as the feature matrix of the feature projection rotated out of the boundary and backward, i.e. the rotation does not affect the feature matrix,
Figure DEST_PATH_IMAGE085
、
Figure 481768DEST_PATH_IMAGE086
from the above feature matrixLAndRtaking a middle value; the flux of the above-mentioned third boundary value
Figure DEST_PATH_IMAGE087
Flux passing through said first boundary value
Figure 49016DEST_PATH_IMAGE042
Second boundary value flux
Figure 81694DEST_PATH_IMAGE080
And feature matrix
Figure 999971DEST_PATH_IMAGE085
、
Figure 759986DEST_PATH_IMAGE086
And calculating to obtain:
Figure 916161DEST_PATH_IMAGE088
further, the third limit value flux described above may be utilized
Figure 244374DEST_PATH_IMAGE087
Simulating the solid-wall boundaries of non-skin meshes, in particularAccording to a third limit value flux
Figure 259734DEST_PATH_IMAGE087
And updating the flow field values of the grid nodes, and simulating the fixed wall boundary of the non-skin grid based on the updated flow field values of the grid nodes. By the steps, boundary information can be added in the flow field numerical simulation of the non-conformal grid, the grid nodes for simulating the solid wall boundary of the non-conformal grid are corrected through the flow field value of the boundary point and the first-order and second-order normal derivatives of the flow field value, and the accuracy of the grid nodes is improved, so that the solid wall boundary of the non-conformal grid can be better simulated under the condition that virtual grid nodes are not required to be arranged.
In summary, in the embodiments of the present invention, a first boundary value flux is obtained based on the flow field value reconstruction of a plurality of grid nodes at a non-close grid solid-wall boundary, and then a first flow field value of a first layer of grid nodes near the boundary is corrected by combining the solid-wall boundary condition and the flow field value of the grid nodes, so as to obtain a corrected second flow field value; and reconstructing based on the corrected second flow field value to obtain a second boundary numerical flux, obtaining a third boundary numerical flux according to the first boundary numerical flux and the second boundary numerical flux, and finally simulating the fixed wall boundary of the non-attached grid by using the third boundary numerical flux so as to introduce boundary information into the numerical simulation of the non-attached grid.
It should be understood that, although the steps in the flowcharts of the figures are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and may be performed in other orders unless explicitly stated herein. Moreover, at least a portion of the steps in the flow chart of the drawings may include multiple sub-steps or multiple stages, which are not necessarily performed at the same time or on the same device or machine, but may be performed at different times and different places, which are not necessarily performed in sequence, but may be performed alternately or alternatingly with other steps or at least a portion of the sub-steps or stages of other steps.
In a second aspect, as shown in fig. 4, fig. 4 is a schematic structural diagram of an embodiment of a non-skin-mesh-based fixed-wall boundary numerical simulation apparatus according to the present invention, and an embodiment of the present invention provides a non-skin-mesh-based fixed-wall boundary numerical simulation apparatus, including:
an obtaining module 401, configured to obtain flow field values of a plurality of grid nodes of a non-skin grid adjacent to a solid wall boundary, where the grid nodes include a first layer of grid nodes near the boundary, and the flow field values include a first flow field value of the first layer of grid nodes;
a reconstruction module 402, configured to reconstruct a flow field value based on the plurality of grid nodes to obtain a first boundary value flux;
a correcting module 403, configured to set a solid wall boundary condition, and combine the solid wall boundary condition with the flow field values of the multiple mesh nodes to correct the first flow field value of the first-layer mesh node, so as to obtain a second flow field value of the first-layer mesh node;
a simulation module 404, configured to obtain a second boundary numerical flux based on the second flow field value reconstruction, obtain a third boundary numerical flux according to the first boundary numerical flux and the second boundary numerical flux, and simulate a solid-wall boundary of the non-skin mesh by using the third boundary numerical flux.
The solid wall boundary numerical simulation device based on the non-skin-like grid provided by the embodiment of the invention can realize each implementation mode in the method embodiment of fig. 1 and corresponding beneficial effects, and is not repeated herein for avoiding repetition.
In a third aspect, an embodiment of the present invention provides a computer device, including: the device comprises a memory, a processor and a computer program which is stored on the memory and can run on the processor, wherein the processor executes the computer program to realize the steps in the non-skin-mesh-based solid wall boundary numerical simulation method.
In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the computer program implements the steps in the non-skin mesh-based fixed wall boundary numerical simulation method.
Specifically, referring to fig. 5, fig. 5 is a schematic diagram of a basic structure of a computer device according to an embodiment of the present invention. The computer device 500 includes a memory 501, a processor 502, and a network interface 503 communicatively coupled to each other via a system bus. It is noted that only a computer device 500 having components 501-503 is shown, but it is understood that not all of the shown components are required to be implemented, and that more or fewer components may be implemented instead. As will be understood by those skilled in the art, the computer device is a device capable of automatically performing numerical calculation and/or information processing according to a preset or stored instruction, and the hardware includes, but is not limited to, a microprocessor, an Application Specific Integrated Circuit (ASIC), a Programmable Gate Array (FPGA), a Digital Signal Processor (DSP), an embedded device, and the like.
The computer device can be a desktop computer, a notebook, a palm computer, a cloud server and other computing devices. The computer equipment can carry out man-machine interaction with a user through a keyboard, a mouse, a remote controller, a touch panel or voice control equipment and the like.
The memory 501 includes at least one type of readable storage medium including a flash memory, a hard disk, a multimedia card, a card type memory (e.g., SD or DX memory, etc.), a Random Access Memory (RAM), a Static Random Access Memory (SRAM), a Read Only Memory (ROM), an Electrically Erasable Programmable Read Only Memory (EEPROM), a Programmable Read Only Memory (PROM), a magnetic memory, a magnetic disk, an optical disk, etc. In some embodiments, the storage 501 may be an internal storage unit of the computer device 500, such as a hard disk or a memory of the computer device 500. In other embodiments, the memory 501 may also be an external storage device of the computer device 500, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), or the like, provided on the computer device 500. Of course, the memory 501 may also include both internal and external memory units of the computer device 500. In this embodiment, the memory 501 is generally used for storing an operating system and various types of application software installed on the computer device 500, such as program codes of a non-conformal grid-based fixed wall boundary numerical simulation method. Further, the memory 501 may also be used to temporarily store various types of data that have been output or are to be output.
Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better implementation manner. Based on such understanding, the technical solutions of the present application or portions thereof that contribute to the prior art may be embodied in the form of a software product, where the computer software product is stored in a storage medium (such as a ROM/RAM, a magnetic disk, and an optical disk), and includes several instructions for enabling a terminal device (which may be a mobile phone, a computer, a server, an air conditioner, or a network device) to execute the method according to the embodiments of the present application.
The above description is intended to be illustrative of the preferred embodiment of the present invention and should not be taken as limiting the invention, but rather, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.

Claims (10)

1. A solid wall boundary numerical simulation method based on non-skin grids is characterized by comprising the following steps:
s1, obtaining flow field values of a plurality of grid nodes of a non-skin grid adjacent to a solid wall boundary, wherein the grid nodes comprise first-layer grid nodes near the boundary, and the flow field values comprise first flow field values of the first-layer grid nodes;
s2, reconstructing flow field values based on the grid nodes to obtain a first boundary value flux;
s3, setting a solid wall boundary condition, combining the solid wall boundary condition with the flow field values of the grid nodes, and correcting the first flow field value of the first layer of grid nodes to obtain a second flow field value of the first layer of grid nodes;
s4, reconstructing based on the second flow field value to obtain a second boundary numerical flux, obtaining a third boundary numerical flux according to the first boundary numerical flux and the second boundary numerical flux, and simulating a solid wall boundary of the non-skin grid by using the third boundary numerical flux.
2. The method of claim 1, wherein the deriving a first boundary value flux based on the flow field value reconstruction of the plurality of grid nodes comprises:
and carrying out eccentric reconstruction on the flow field values of the grid nodes to obtain the first boundary value flux.
3. The method of claim 2, wherein the flow field values of the grid nodes comprise original flow field values, the step of setting a fixed-wall boundary condition, and combining the fixed-wall boundary condition with the flow field values of the plurality of grid nodes to modify the first flow field values of the first layer of grid nodes to obtain the second flow field values of the first layer of grid nodes comprises:
determining boundary nodes corresponding to the first layer of grid nodes on a fixed wall boundary, so that the connecting line direction of the first layer of grid nodes and the boundary nodes is the external normal direction of the fixed wall boundary;
acquiring original flow field values of a plurality of grid nodes close to the boundary node, wherein the original flow field values comprise first flow field values of the first layer of grid nodes;
calculating the original flow of the boundary node by extrapolation method based on the original flow field values of the plurality of grid nodesField values and their first and second boundary normal derivatives
Figure DEST_PATH_IMAGE001
、
Figure 952267DEST_PATH_IMAGE002
；
The original flow field value and the first and second derivatives of the boundary node are obtained
Figure 173164DEST_PATH_IMAGE001
、
Figure 526785DEST_PATH_IMAGE002
Rotating to the external normal direction of the solid wall boundary to obtain the rotating flow field value of the boundary node and the first-order and second-order normal derivatives thereof
Figure DEST_PATH_IMAGE003
、
Figure 731501DEST_PATH_IMAGE004
；
Rotational flow field values to the boundary nodes
Figure DEST_PATH_IMAGE005
And performing characteristic projection on the first-order and second-order normal derivatives of the boundary nodes to obtain the rotating flow field projection values of the boundary nodes and the first-order and second-order normal derivatives of the boundary nodes
Figure 868084DEST_PATH_IMAGE006
、
Figure DEST_PATH_IMAGE007
；
The boundary point on the fixed wall boundary
Figure 740225DEST_PATH_IMAGE008
Is set to zero, in conjunction with the boundary nodeAdjusting the rotary flow field value of the projection value of the rotary flow field of the point
Figure 140114DEST_PATH_IMAGE005
Setting the pressure normal derivative of the boundary node on the fixed wall boundary according to a centripetal force formula, and adjusting the first normal derivative of the rotational flow field value of the boundary node by combining the first normal derivative of the rotational flow field projection value of the boundary node;
carrying out Taylor series expansion on the adjusted rotating flow field value of the boundary node along the external normal direction of the solid wall boundary to obtain the rotating flow field value of the first layer of grid nodes;
and obtaining a second flow field value of the first-layer grid node according to the rotating flow field value of the first-layer grid node.
4. The method of claim 3, wherein the adjusted rotational flow field values of the boundary nodes are subjected to Taylor series expansion along the outer normal direction of the solid wall boundary to obtain the first layer of grid nodesPThe step of rotating the flow field value of (2) comprises:
calculating a length between the first-tier mesh node and the boundary nodeh；
The rotational flow field value, the first normal derivative, the second normal derivative, and the length based on the boundary nodeshComputing the first-tier mesh nodesPThe rotational flow field value of (a).
5. The method of claim 4, wherein said passing through said first level mesh nodesPThe obtaining of the second flow field value of the first-layer mesh node by the rotating flow field value includes:
connecting the first layer mesh nodePThe rotating flow field value is rotated to the original direction from the external normal direction of the solid wall boundary, and a second flow field value of the first layer of grid nodes after correction is obtained.
6. The method of any of claim 5, wherein reconstructing based on the second flow field values to obtain a second boundary value flux, and obtaining a third boundary value flux from the first boundary value flux and the second boundary value flux comprises:
carrying out eccentric reconstruction on the basis of the second flow field value corrected by the first layer of grid nodes to obtain a second boundary numerical flux;
acquiring a feature matrix of a first flow field value before the first layer of grid nodes are corrected;
and calculating to obtain the third boundary value flux based on the first boundary value flux, the second boundary value flux and the feature matrix.
7. The method of claim 1, wherein the step of simulating the solid wall boundary of the non-skin mesh using the third boundary numerical flux comprises:
and updating the flow field value of the grid node according to the flux of the third boundary value, and simulating the fixed wall boundary of the non-skin grid based on the updated flow field value of the grid node.
8. A solid wall boundary numerical simulation device based on non-skin-type grids is characterized by comprising:
the device comprises an acquisition module, a data processing module and a data processing module, wherein the acquisition module is used for acquiring flow field values of a plurality of grid nodes of a non-skin grid adjacent to a solid wall boundary, the grid nodes comprise first-layer grid nodes near the boundary, and the flow field values comprise first flow field values of the first-layer grid nodes;
the reconstruction module is used for reconstructing flow field values based on the grid nodes to obtain a first boundary value flux;
the correction module is used for setting a solid wall boundary condition, combining the solid wall boundary condition with the flow field values of the grid nodes, correcting the first flow field value of the first layer of grid nodes, and obtaining a second flow field value of the first layer of grid nodes;
and the simulation module is used for reconstructing based on the second flow field value to obtain a second boundary numerical flux, obtaining a third boundary numerical flux according to the first boundary numerical flux and the second boundary numerical flux, and simulating the solid-wall boundary of the non-skin mesh by using the third boundary numerical flux.
9. A computer device, comprising: memory, processor and computer program stored on the memory and executable on the processor, the processor implementing the steps in the non-skin mesh based solid wall boundary numerical simulation method according to any one of claims 1 to 7 when executing the computer program.
10. A computer-readable storage medium, having stored thereon a computer program which, when being executed by a processor, carries out the steps of the non-skin mesh-based fixed-wall boundary numerical simulation method according to any one of claims 1 to 7.
CN202211254384.0A 2022-10-13 2022-10-13 Solid wall boundary numerical simulation method based on non-body-attached grid and related equipment Pending CN115563898A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116245049A (en) * 2023-05-11 2023-06-09 中国空气动力研究与发展中心计算空气动力研究所 Node type non-structural grid boundary correction method, device, equipment and medium

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116245049A (en) * 2023-05-11 2023-06-09 中国空气动力研究与发展中心计算空气动力研究所 Node type non-structural grid boundary correction method, device, equipment and medium

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