CN111444661B - Method for eliminating warping phenomenon in interactive prism grid generation - Google Patents
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Abstract
The invention discloses a method for eliminating warping phenomenon in interactive prism grid generation, namely, firstly, manually and interactively generating a space propulsion grid of object plane grid boundary points, and then, utilizing a fairing algorithm to propel the object plane grid boundary points to have normal vectors inX、Y、ZSmoothing components in three coordinate directions, then interpolating by a radial basis function method to obtain a space propulsion grid of an object plane grid internal point, and finally assembling to obtain a boundary layer prism grid for CFD calculation simulation; the method optimizes the object plane grid boundary space push plane grid generated by manual interaction, eliminates the influence of warping phenomenon on the quality of the prism grid by adopting technologies such as normal vector fairing, radial basis function interpolation and the like, and has obvious technical advantages in the aspect of improving the generation efficiency of the prism grid and the universality of the method.
Description
Technical Field
The present invention relates to the field of grid generation for numerical computation, and in particular to the field of prismatic grid generation in Computational Fluid Dynamics (CFD).
Background
With the rapid development of computer hardware technology and computational methods, computational Fluid dynamics (cfd) plays an increasingly important role in scientific research and industrial product design, and is widely used for numerical simulation of true flows of various complex shapes. Particularly in the aerospace field, CFD has become an important tool for aircraft performance analysis and design.
And the CFD disperses the space flow field of the simulation object based on the grid, and then solves a discrete mathematical equation to obtain a numerical flow field of the simulation object under a specific condition. The quality of discrete grids is a key factor influencing the efficiency, convergence and precision of CFD numerical solution. The high-quality flow field calculation grid can better approximate the real flow phenomenon, the convergence rate of flow field calculation can be greatly improved, and the cost of CFD simulation is reduced.
According to the topological relation of the mesh, the CFD computational mesh can be divided into two categories: structural meshes and non-structural meshes. The structural grid has the advantages of good quality, simple data structure and the like, but the generation of the structural grid with complex appearance is very difficult, and a great deal of manpower is required to design the grid topology and adjust the grid quality. Unstructured mesh can simulate arbitrary complex shapes, but does not work well to simulate viscous flow dominated by boundary layer effects.
Therefore, a hybrid mesh technique combining the respective advantages of the unstructured mesh and the structured mesh has become an important research direction in the field of mesh generation. The semi-structured prism grid has better adaptability to complex shapes, can make up the defect of simulating viscous flow of non-structured triangular/tetrahedral grids, has better flow prediction precision, and is a research hotspot in the field of grid generation at present.
At present, the generation of the semi-structured prismatic grid has two ideas, one typical idea is to develop towards the direction of automation by adopting an integral generation mode, but the grid quality cannot be locally adjusted, the grid generation parameters have large dependence on the appearance, the grid density distribution and the like, and the optimal parameters need to be obtained by repeated attempts; the other idea is that the interactive prismatic grid generation method based on boundary point space propulsion grid constraint, which is proposed by Sunji and the like [1], can obtain high-quality prismatic grids through manual interactive adjustment. The second idea is to generate or modify the space propulsion grids of the object plane grid boundary points in a manual interaction mode, so that the propulsion direction, the propulsion speed and the local grid quality of the prism grids are adjusted and controlled, and the time consumption for adjusting the prism grid quality is reduced to a certain extent. For the appearance with rapid curvature change, the interactive method can amplify the displacement at the boundary out of order and transmit the displacement to the inner area, so that the generated prism grid is warped, the quality of the prism grid is reduced, and even the grid is distorted to generate a negative volume. Document [1] proposes that the warpage of the prism lattice can be eliminated and the quality of the prism lattice can be improved by adding a space to advance the planar lattice. However, the space propulsion surface grid is added inside, on one hand, the difficulty of pretreatment work and prism grid generation is greatly increased, the universality of the method is reduced, on the other hand, the number of radial base points is increased, and the calculation amount of displacement interpolation and the time cost consumption are increased.
[1] Sun rock, interactive prismatic grid generation method [ J ] CAD and graphic bulletin 2016,28(2): 247-.
Disclosure of Invention
The invention aims to provide a method for eliminating warping phenomenon in interactive prism grid generation, aiming at the conditions that the method for eliminating warping phenomenon by adding a space propulsion surface grid at a local position of an object plane grid is poor in universality and algorithm difficulty is increased, a normal vector is propelled to an object plane grid boundary point through a fairing method to conduct fairing, and discontinuous amplification propagation of the normal vector propelled to the object plane grid boundary point in a space is eliminated, so that the warping phenomenon of the prism grid is avoided, and the robustness of the interactive prism grid generation method and the adaptability to complex shapes can be greatly improved.
The invention also has the purpose of correcting the influence of object plane grid boundary point propulsion normal vector errors on the generation of the prism grid, improving the quality of the prism grid and improving the accuracy and the calculation efficiency of numerical simulation.
In order to achieve the purpose, the invention adopts the following technical scheme:
firstly, based on the boundary ridge of the object plane grid, a space propulsion grid of grid points on the boundary ridge of the object plane grid is generated through manual interaction.
Secondly, the advancing direction and the advancing length of the object plane grid boundary point are extracted to obtain an advancing normal vector N of the object plane grid boundary point, and the advancing normal vector N is decomposed to X, Y, Z three-coordinate directions and is respectively represented as Nx, Ny and Nz.
Then, the curve distance d of the opposite end positions of the grid points on the ridge line of the object plane grid boundary is calculated, and then the curve distance d is divided by the curve length L of the ridge line to obtain the relative positions S of the grid points on the ridge line.
The curve distance d of the opposite end points can be added together by adopting a linear accumulation mode:
wherein d isiIs the curve distance of the ith point from the end point position; x is the number ofiiA coordinate vector for the ii point; np is the number of grid points on the ridge. The distance between any two adjacent points can be expressed as
xii,yii,ziiRespectively 3 coordinate components of the ii object plane grid boundary points.
The curve length L of the ridge line is dnpThe relative position S of the grid points on the ridge can therefore be expressed as:
Si＝di/L i＝1,2,L,np
wherein S isiIs the relative position of the ith grid point on the boundary edge of the object plane grid.
Then, according to the distribution of Nx, Ny, Nz with respect to S, the Nx, Ny, Nz are smoothed by a smoothing method (here, the laplace algorithm is adopted but not limited to be adopted), and then a new object plane grid boundary point propulsion normal vector N' is obtained by combination. The calculation formula of the optic normal vector of the Laplace algorithm is as follows:
wherein, Pi＝[Si,Xi]Is a coordinate vector, X represents any component of the object plane grid boundary point advancing normal vector N in the X, Y, Z three-coordinate direction; t represents the number of iterations; lambda epsilon (0,1) is a fairing coefficient; l (P)i) Represents a laplace displacement vector; np is object plane gridThe number of grid points on the boundary ridge.
And then, calculating the distribution rule of the normal propulsion grid points according to the coordinates of the propulsion grid points of the object plane grid boundary space, and calculating to obtain a new propulsion grid of the object plane grid boundary space by using a propulsion normal vector N' of the new object plane grid boundary points after fairing.
The distribution rule of the advancing grid points can be expressed as:
vk＝Lk/Lm k＝0,1,L,m
wherein, L is the advancing step length of the advancing grid point, the subscript k represents the advancing layer number, and the object plane grid is defined as the 0 th layer; m is the total number of propelling layers; x is the number ofk,yk,zkAdvancing the grid point's 3 coordinate components for the k-th layer, here (x)0,y0,z0) Representing object plane grid points; v is the distribution position of the advancing grid point.
The grid point positions on the new object plane grid bounding space pushing plane grid can be expressed as:
Xk＝X0+vkN′ k＝0,1,L,m
wherein X ═ X1,x2,…,xn]TA grid point coordinate vector list is obtained, subscript k represents the number of propulsion layers, and n is the number of boundary points of an object plane grid; x0Representing a list of object plane grid boundary point coordinate vectors; m is the number of prism grid space propelling layers; n' advances the normal vector for the new object plane grid boundary points.
And then, interpolating by using a radial basis function, taking the grid point of the current layer on the object plane grid boundary space propulsion plane grid as a base point, and obtaining the grid point of the space prism in the corresponding layer by interpolation, and repeating the steps until the positions of the space prism grid points of all the propulsion layers are obtained.
And finally, establishing a connection relation among all grid points, constructing prism grid units, calculating the quality of each grid unit, and evaluating whether the generated boundary layer prism grid meets the requirements of CFD flow field analysis.
In the generation process of the interactive prism grids, the space propulsion grid points of the internal points of the object plane grids are obtained through radial basis function interpolation based on the space propulsion displacement of the boundary points of the object plane grids. The warping phenomenon in the generation of the prism grid is caused by that the space of boundary points of the object plane grid is pushed and distributed inaccurately and propagates and amplifies towards the inside through radial basis interpolation. Therefore, ensuring that the object plane grid boundary points advance normal vector fairing is the key to eliminating the warping of the prism grid.
Based on the principle, the method for eliminating the warping phenomenon in the generation of the interactive prism grid has the core idea that the propulsion normal vector of the object plane grid boundary point is smoothed by a smoothing method. The idea directly operates the space propulsion grids of the boundary points of the object plane grids, the workload of manual processing can be greatly reduced, the generation efficiency of the prism grids is improved, and the engineering practicality of interactive prism grid generation is improved.
Compared with the existing method for eliminating the warping phenomenon of the prism grids, the method for eliminating the warping phenomenon by improving the object plane grid boundary space propelling plane grids provided by the invention utilizes the fairing algorithm to eliminate the influence of the warping phenomenon on the quality of the prism grids, and achieves the following effects:
the object plane grid boundary point is optimized by advancing the normal vector, so that the pretreatment work and the prism grid generation difficulty are avoided being greatly increased, the universality of the method is improved, and the method has important application value.
The warping phenomenon eliminating method provided by the invention can not increase the number of base points for post-processing radial basis function interpolation, avoids increasing the calculation amount of displacement interpolation, and can obviously reduce the time cost consumption for generating the prism grids, thereby improving the operation efficiency of the prism grid generating algorithm.
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The invention will now be described, by way of example, with reference to the accompanying drawings, in which:
FIG. 1 shows a method for eliminating the warpage of prism grids;
FIG. 2 an object plane grid and a boundary space marching plane grid;
wherein: 1 is an object plane grid; 2 is object plane grid boundary ridge; 3, object plane grid boundary space propulsion plane grid; 4 is the object plane grid boundary point; 5, advancing normal vector of the boundary point of the object plane grid before fairing; and 6 is the advancing normal vector of the boundary points of the smooth object plane grids.
Detailed Description
All of the features disclosed in this specification, or all of the steps in any method or process so disclosed, may be combined in any combination, except combinations of features and/or steps that are mutually exclusive.
Any feature disclosed in this specification (including any accompanying claims, abstract and drawings), may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.
The implementation combines fig. 1-2 to describe in detail the specific implementation process of the adopted technical scheme:
in step (1), for a given object plane grid 1, the boundary ridge 2 of the object plane grid is found by using the boundary information, and grid points on the boundary ridge, that is, object plane grid boundary grid points, are recorded.
Step (2): and respectively generating object plane grid boundary space propelling plane grids 3 on object plane grid boundary edge lines in a manual interaction mode.
Step (3): and (3) acquiring a propulsion normal vector of the boundary point of the object plane grid by using the space propulsion plane grid obtained in the step (2), and decomposing the propulsion normal vector to X, Y, Z three-coordinate directions, wherein the propulsion normal vector is respectively represented as Nx, Ny and Nz.
Step (4): by utilizing the coordinate information of the grid points on the object plane grid boundary ridge, firstly, the curve distance d of the opposite end positions of the object plane grid boundary point is calculated, and then the curve distance d is divided by the length L of the ridge, so that the relative position S of the grid points on the ridge is obtained.
Step (5): firstly, based on the calculation result in the step (4), the distribution conditions of Nx, Ny, Nz relative to S are respectively obtained, then, by using a fairing method, the embodiment adopts laplace algorithm fairing, but the method is not limited to adopt the specific fairing method, the Nx, Ny, Nz are respectively faired, and a new object plane grid boundary point propulsion normal vector is obtained by using the combination of the Nx, Ny, Nz after fairing.
Step (6): and calculating to obtain a new object plane grid boundary space propelling surface grid by utilizing the propulsion normal vector of the object plane grid boundary points after fairing according to the distribution rule of the propelling grid points on the object plane grid boundary space propelling surface grid.
Step (7): and (3) by utilizing a radial basis function interpolation method, interpolating to obtain internal space prism grid points of corresponding layers by taking the grid points of the current propulsion layer on the new object plane grid boundary space propulsion plane grid as radial basis points, and circulating along the propulsion layer until the space prism grid point positions of all the propulsion layers are obtained.
Step (8): firstly, generating a spatial prism grid based on the connection relation among all grid points; and then judging whether the prism grids have the warping phenomenon, if so, repeating the steps (5) to (7) until the obtained prism grids do not have the warping phenomenon.
Step (9): and (4) inspecting the quality of the prism grids by using a grid quality detection method, outputting a prism grid warping phenomenon elimination effect evaluation report, and ending the process.
In the embodiment, an object plane grid boundary space propelling plane grid is generated through manual interaction, then the propelling normal vector of the extracted object plane grid boundary points is decomposed, the distribution condition of the propelling normal vector component is obtained by calculating the relative positions of the object plane grid boundary points on the boundary ridge, then the propelling normal vector components of the object plane grid boundary points are respectively subjected to fairing by a curve fairing method, the propelling normal vector of the object plane grid boundary points is used for updating the object plane grid boundary space propelling plane grid, then the space prism grid is obtained through radial basis function interpolation, and the warping phenomenon in the generation of the interactive prism grid is eliminated.
The invention is not limited to the foregoing embodiments. The invention extends to any novel feature or any novel combination of features disclosed in this specification and any novel method or process steps or any novel combination of features disclosed.
Claims (4)
1. A method for eliminating warping phenomenon in interactive prism grid generation is characterized by comprising the following steps:
s1: based on the boundary edge lines of the object plane grids, generating space propulsion grids of grid points on the boundary edge lines of the object plane grids through manual interaction;
s2: by utilizing the space propulsion grid, the propulsion direction and the propulsion length of the boundary points of the object plane grid are extracted according to the object plane grid boundary space propulsion plane grid generated by manual interaction, and the propulsion normal vector of the boundary points of the object plane grid is obtained
And is decomposed intoX、Y、ZIn the three coordinate directions, are respectively expressed as
；
S3: obtaining the distribution condition of the propulsion normal vector component by calculating the relative position of the object plane grid boundary point on the boundary ridge;
s4: by using the fairing algorithm, the normal vector is pushed to the boundary point of the object plane gridX、Y、ZComponent in three coordinate directions
Smoothing is carried out to obtain a new object plane boundary grid point propulsion normal vector
；
S5: calculating the distribution rule of the normal propulsion grid points according to the coordinates of the propulsion grid points of the object plane grid boundary space:
wherein,
index for advancing step size of grid point
Representing the number of the advancing layers, and defining an object plane grid as a 0 th layer;
the total number of propulsion layers;
is as follows
3 coordinate components of layer advance grid points, herex 0,y 0,z 0) Representing object plane grid points;vin order to advance the distribution position of the grid points,
and the new object plane boundary grid points are utilized to advance the normal vector
Calculating to obtain a new object plane boundary space propelling plane grid, wherein the grid point position is expressed as:
wherein,
for a list of grid point coordinate vectors, subscripts
Indicating the number of propulsion layers, here
The number of boundary points of the object plane grid is;
a coordinate vector list of object plane grid boundary points is obtained;
advancing the number of layers for the prism grid space;
advancing the normal vector for the new object plane grid boundary points;
s6: obtaining a space propulsion grid of an internal point of the object plane grid through interpolation by a radial basis function method;
s7: establishing connection relations among all grid points, constructing prism grid units, calculating the quality of each grid unit, and judging whether the generated boundary layer prism grid meets the requirements of CFD flow field analysis.
2. The method of claim 1, wherein the step of S3 comprises using a curve distance between grid points on a ridge line of the boundary of the object plane grid and opposite end points of the grid pointsdDivided by the length of the curve of the ridgeLObtaining the relative position of the grid points on the ridgeSDistance of curve from end pointdAnd (3) adding the distances of each line segment together in a linear accumulation mode:
wherein,
is the first
The curve distance of the point from the end point position;
is as follows
Coordinate vectors of the points;
the number of grid points on the ridge line.
3. The method of claim 2, wherein the step of eliminating warping in the generation of interactive prismatic grids comprises,
distance between any two adjacent points:
wherein
,
,
Are respectively the first
The 3 coordinate components of the individual object plane grid boundary points,
curve length of ridge:
，
relative position of grid points on ridgeSComprises the following steps:
。
4. the method of claim 1, wherein the warping phenomenon is eliminated in the generation of interactive prismatic grids, and the method comprises the following steps: and (4) interpolating by utilizing a radial basis function, taking the grid point of the current layer on the object plane grid boundary space propulsion plane grid as a base point, obtaining the grid point of the space prism in the corresponding layer by interpolation, and repeating the steps until the space prism grid point positions of all propulsion layers are obtained.
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