CN-121435632-B - Self-adaptive generation method, device, equipment and medium for path protection curved edge P2 grid

CN121435632BCN 121435632 BCN121435632 BCN 121435632BCN-121435632-B

Abstract

The invention discloses a self-adaptive generation method, device, equipment and medium for a path-preserving curved edge P2 grid, and belongs to the technical field of numerical simulation. The method comprises the steps of constructing a Riemann measurement field for controlling P2 interpolation errors according to high-order derivatives of a physical field function, generating boundary points and internal points based on the measurement field, recording a generation path between each internal point and a generation source point, executing constrained Delaunay triangulation by taking the generation path as a constraint edge to generate an initial straight edge grid, bending the straight edge into a P2 curved edge by solving a constrained optimization problem, optimizing the target to minimize the length of a curved edge geodesic line, and ensuring that the bent element shape is effective. The invention solves the problems of insufficient resolution of an anisotropic region and easy failure of a curved unit through a physical driving measurement field, a topology maintenance generation path and a technical closed loop of geometric effective curved optimization, and improves the precision and stability of high-order numerical simulation.

Inventors

ZHANG RUILI
ZHANG SHENGQI

Assignees

宁波数字孪生(东方理工)研究院

Dates

Publication Date: 20260508
Application Date: 20251229

Claims (10)

1. A self-adaptive generation method of a path protection curved edge P2 grid is characterized by comprising the steps of coupling analysis of shock waves and a thermal protection system in a head area of a hypersonic aircraft in the process of reentering an atmosphere; The method comprises the steps of inputting a two-dimensional or three-dimensional geometric model of an aircraft head, obtaining a flow field solution comprising strong bow shock waves and a high-temperature boundary layer around the head through primary low-precision initial calculation, constructing a Riemann metric field for controlling P2 interpolation errors according to a high-order derivative of a physical field function to be solved, and calculating a Riemann metric tensor of the whole flow field according to gradients, second-order and third-order derivatives of temperature and pressure fields; The method comprises the steps of carrying out self-adaptive boundary point sampling on the surface of an aircraft, generating boundary points and interior points in a calculation domain based on a Riemann metric field, recording a generation path connecting the new interior points and a generation source point in the process of generating each new interior point, wherein the generation source point is an existing interior point or boundary point when the new interior point is generated; taking the generated boundary points and the internal points as input, taking all the generated paths after the crossing road is removed as constraint edges, executing Delaunay triangulation with constraint, and generating an initial straight-edge grid; The method comprises the steps of bending straight edges in an initial straight edge grid into P2 curved edges, calculating space coordinates of midpoints used for constructing the P2 curved edges by solving an optimization problem with constraint for each straight edge to be bent, wherein the optimization problem is solved for minimizing the geodesic length of the P2 curved edges, and the constraint condition of the optimization problem is that all adjacent grid units sharing the straight edges to be bent keep the shape valid after bending.
2. The method for adaptively generating the path-preserving curved edge P2 grid according to claim 1, wherein the method for constructing the Riemann metric field for controlling the P2 interpolation error according to the higher derivative of the physical field function to be solved comprises the following steps: Establishing an interpolation error model on the P2 curved edge unit based on third-order derivative, curvature and gradient of the physical field function to be solved; According to a preset uniform target error value, reversely solving the ideal grid size of each point in the calculation domain in the local gradient direction and the local contour line direction from the interpolation error model; The method comprises the steps of marking a unit vector in a local gradient direction as a first base vector, marking a unit vector in a local contour line direction as a second base vector, calculating the inverse square of an ideal grid size corresponding to the first base vector as a first matrix element, calculating the inverse square of an ideal grid size corresponding to the second base vector as a second matrix element, forming a base matrix by the first base vector and the second base vector, constructing a diagonal matrix by the first matrix element and the second matrix element as diagonal elements, and multiplying the base matrix, the diagonal matrix and a transposed matrix of the base matrix in sequence to obtain a product result as a Riemann metric tensor of points.
3. The method for adaptively generating the path-preserving curved edge P2 grid according to claim 2, wherein the boundary points and the interior points are generated in the calculation domain based on the Riemann metric field, comprising the steps of: Calculating the geodesic length of the boundary by utilizing a Riemann metric field aiming at each boundary of the calculation domain, rounding the geodesic length to the nearest integer to obtain the number of boundary segments, uniformly dividing the boundary into a plurality of segments according to the number of boundary segments, and generating boundary points at segment points; and recording a generation path connecting the new internal points and a generation source point in the process of generating each new internal point.
4. The method for adaptively generating the path-preserving curved edge P2 grid according to claim 3, wherein the internal points are generated from the boundary points to the inside of the calculation domain by adopting a front edge pushing algorithm, comprising the following steps: Taking a current point from a front propulsion queue containing boundary points as a generation source point; Aiming at a plurality of different candidate direction numbers N p , respectively executing a test flow, namely calculating N p evenly distributed emergent directions corresponding to the current candidate direction number, solving a geodesic equation along each emergent direction based on a Riemann metric field, generating a circle of candidate points, carrying out local virtual triangulation on the generated source points and the candidate points, and evaluating the unit quality of all grid units after the dissection; selecting a direction number optimal for the unit quality obtained by the evaluation from among all the attempted direction numbers as an optimal direction number N p_opt ; based on the Riemann metric field, generating actual new interior points along the direction corresponding to the optimal number of directions N p_opt , and recording a generating path for connecting each new interior point with the generating source point.
5. The method for adaptively generating the path-preserving curved edge P2 grid according to claim 4, wherein the internal points are generated from the boundary points to the inside of the calculation domain by using a front edge advancing algorithm, further comprising the steps of: A rejection check is performed for each newly generated point, including whether the newly generated interior point is inside the computation domain and calculating geodesic distances of the interior point from all existing points based on the Riemann metric field, the point being added to the front push queue only if the newly generated point is inside the computation domain and the geodesic distance is greater than a preset threshold.
6. The adaptive generation method of a guaranteed path curved edge P2 grid according to claim 5, wherein the generated boundary points and internal points are used as inputs, all generated paths after the crossing is removed are used as constraint edges, and Delaunay triangulation with constraint is performed to generate an initial straight-edge grid, and the method specifically comprises the following steps: acquiring all generated boundary points, all generated internal points and all recorded generation paths; Setting all the generated paths as constraint edges which must be reserved after the cross paths are removed; Performing constrained Delaunay triangulation based on boundary points and internal points, wherein the set constraint edges are forcedly reserved as undeletable edges in the subdivision process; An initial straight-sided mesh generated by triangulation is output that contains all the constraint sides.
7. The method for adaptively generating the path-preserving curved edge P2 grid according to claim 6, wherein the step of bending the straight edge in the initial straight edge grid into the P2 curved edge comprises the steps of: Traversing straight edges in the initial straight edge grid, and defining space coordinates of midpoints of the straight edges to be bent as optimization variables for each straight edge to be bent; The length of the geodesic line of the P2 curved edge formed by the straight edge to be bent after bending in the Riemann measuring field is minimized as a target, and an objective function of an optimization problem is constructed; constraint conditions of the optimization problem include that all adjacent grid cells sharing a straight edge to be bent are positive everywhere in the jacobian after bending; And updating the straight edge to be bent into a P2 curved edge according to the optimal midpoint coordinate.
8. The self-adaptive generation device for the path protection curved edge P2 grid is characterized by comprising the step of coupling analysis of shock waves and a thermal protection system in the head area of a hypersonic aircraft in the process of reentering an atmosphere; The Riemann measurement field construction module is used for inputting a two-dimensional or three-dimensional geometric model of the head of the aircraft, obtaining a flow field solution containing strong bow shock waves and a high-temperature boundary layer around the head through one-time low-precision initial calculation, constructing a Riemann measurement field for controlling P2 interpolation errors according to a high-order derivative of a physical field function to be solved, and calculating a Riemann measurement tensor of the whole flow field according to gradients, second-order and third-order derivatives of a temperature and pressure field; The system comprises a point generation module, a calculation domain, a point generation module and a point generation module, wherein the point generation module is used for carrying out self-adaptive boundary point sampling on the surface of an aircraft and is used for generating boundary points and interior points in a calculation domain based on a Riemann metric field; The grid construction module is used for taking the generated boundary points and the internal points as input, taking all the generated paths after the crossing road is removed as constraint edges, and executing Delaunay triangulation with constraint to generate an initial straight-edge grid; The straight edge bending module is used for bending straight edges in the initial straight edge grids into P2 curved edges, wherein for each straight edge to be bent, space coordinates of a middle point used for constructing the P2 curved edges are calculated by solving an optimization problem with constraint, the solving goal of the optimization problem is to minimize the geodesic length of the P2 curved edges, and the constraint condition of the optimization problem is that all adjacent grid units of the straight edges to be bent are shared, and the shape is kept valid after bending.
9. An electronic device comprising a processor and a memory, the processor being configured to execute a computer program stored in the memory to implement the path preserving curved P2 grid adaptive generation method of any of claims 1 to 7.
10. A computer-readable storage medium storing at least one instruction that when executed by a processor implements the path preserving curved P2 grid adaptive generation method of any of claims 1 to 7.

Description

Self-adaptive generation method, device, equipment and medium for path protection curved edge P2 grid Technical Field The invention belongs to the technical field of numerical simulation, and particularly relates to a self-adaptive generation method, device, equipment and medium for a path-preserving curved edge P2 grid. Background In the fields of engineering and scientific computation such as aerospace, automobile design, weather forecast and the like, a high-order finite element method has become a mainstream numerical simulation method due to high-precision and rapid convergence characteristics. The method relies on high quality curved-edge grids to accurately fit complex geometric boundaries and improve computational accuracy. In the prior art, the anisotropic grid self-adaptation technology generally guides the generation of straight-edge grids through a preset measurement field, and curved-edge grids are obtained by simply bending the straight-edge grids, so that invalid grid units are easy to generate, and the precision and stability of high-order numerical simulation are affected. Disclosure of Invention The invention aims to provide a self-adaptive generation method, device, equipment and medium for a path-preserving curved edge P2 grid, which at least solve or improve the problems in the background technology. In order to achieve the above purpose, the present invention adopts the following technical scheme: the invention provides a self-adaptive generation method of a path-preserving curved edge P2 grid, which comprises the following steps: constructing a Riemann metric field for controlling the P2 interpolation error according to the high-order derivative of the physical field function to be solved; Recording a generation path connecting the new internal points and a generation source point in the process of generating each new internal point, wherein the generation source point is an existing internal point or boundary point when the new internal point is generated; taking the generated boundary points and the internal points as input, taking all the generated paths after the crossing road is removed as constraint edges, executing Delaunay triangulation with constraint, and generating an initial straight-edge grid; The method comprises the steps of bending straight edges in an initial straight edge grid into P2 curved edges, calculating space coordinates of midpoints used for constructing the P2 curved edges by solving an optimization problem with constraint for each straight edge to be bent, wherein the optimization problem is solved for minimizing the geodesic length of the P2 curved edges, and the constraint condition of the optimization problem is that all adjacent grid units sharing the straight edges to be bent keep the shape valid after bending. According to the scheme, a Riemann metric field is constructed, boundary points and internal points are generated, and technical closed loops of generating paths, constraint triangulation, straight edge optimization, straight edge bending and curved edge optimization are recorded. On one hand, the physical field high-order derivative is utilized to guide grid generation, on the other hand, the physical anisotropic topology is ensured not to be destroyed in the grid connection stage by reserving a generation path, and finally, the effectiveness of a high-order Qu Bian unit is ensured by optimizing bending with constraint, so that the efficiency, the precision and the stability of high-order simulation are integrally considered. Because the guidance of the Riemann metric field is strictly followed in the point generation and grid connection stages, the finally generated grid can form units orderly arranged along the main direction in the region with intense physical field gradient, and better resolution is provided, so that interpolation errors are reduced. The curve Bian Zhongdian coordinates are determined by solving the optimization problem with constraint, the jacobian of all units after bending is ensured to be positive everywhere in a mathematically strict mode, the generation of invalid units is thoroughly avoided, and a solid foundation is laid for the stable solution of high-order finite element calculation. Further, according to the higher derivative of the physical field function to be solved, a Riemann metric field for controlling the P2 interpolation error is constructed, which comprises the following steps: Establishing an interpolation error model on the P2 curved edge unit based on third-order derivative, curvature and gradient of the physical field function to be solved; According to a preset uniform target error value, reversely solving the ideal grid size of each point in the calculation domain in the local gradient direction and the local contour line direction from the interpolation error model; The method comprises the steps of marking a unit vector in a local gradient direction as a first base vector, marking a unit vector i