Two-dimensional high-order grid generation method based on partial differential equation solving

A technology for partial differential equations and grid generation, which is applied in special data processing applications, complex mathematical operations, geometric CAD, etc. It can solve problems such as consumption, multiple time resources and computing resources, and difficulty in adapting to the needs of high-order grid generation.

Pending Publication Date: 2021-01-05
HANGZHOU DIANZI UNIV
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Problems solved by technology

Most of the existing high-order grid generation methods rely on global iterative solutions, which consume more time and computing resources, and are difficult to adapt to the large-scale high-order grid generation requirements in industry

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  • Two-dimensional high-order grid generation method based on partial differential equation solving
  • Two-dimensional high-order grid generation method based on partial differential equation solving
  • Two-dimensional high-order grid generation method based on partial differential equation solving

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Embodiment Construction

[0048] The present invention will be further described below in conjunction with accompanying drawing.

[0049] A two-dimensional high-order grid generation method based on solving partial differential equations, the specific steps are as follows:

[0050] Step 1. Generate a linear grid covering the two-dimensional geometric model of the aircraft wing according to the two-dimensional geometric model of the aircraft wing, and establish a mapping relationship between the boundary of the linear grid and the boundary of the two-dimensional geometric model of the aircraft wing, as follows:

[0051] Such as figure 1 As shown, input the two-dimensional geometric model of the aircraft wing shape, (using the existing low-order mesh generation method) to generate a relatively sparse linear triangular mesh covering the two-dimensional geometric model of the aircraft wing shape, such as figure 2 As shown, record the line unit at the boundary of the linear triangular mesh as ΔL j ,j∈[1,...

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Abstract

The invention discloses a two-dimensional high-order grid generation method based on partial differential equation solving. At present, generation of high-quality and high-precision high-order grids is still an open problem. The method comprises the following steps: firstly, generating a linear grid covering the two-dimensional geometrical model of the aircraft wing shape, and establishing a mapping relationship between the boundary of the linear grid and the boundary of the two-dimensional geometrical model of the aircraft wing shape; then, ascending the order of the linear grid, establishinga partial differential equation for controlling an internal grid point offset vector field by taking an ascending order linear grid boundary offset vector as a constraint, and solving the partial differential equation by adopting a high-order boundary element numerical method; and finally, shifting all grid points of the ascending order linear grid along respective corresponding shifting vectors,and representing each shifted line unit in a high-order geometrical form to obtain a high-order grid. The method effectively improves the precision and speed of obtaining the offset vector field, andachieves the quick generation of high-quality high-order grid units as few as possible based on the airplane wing shape model.

Description

technical field [0001] The invention relates to a high-precision grid generation process in preprocessing in the field of numerical simulation, in particular to a two-dimensional high-order grid generation method based on PDE solution. Background technique [0002] Mesh generation is a preprocessing process in numerical simulation techniques such as finite element method, finite volume method, and finite difference method. This process divides a continuous geometric area into a combination of finite basic geometric shapes. These basic geometric shapes are called grids. cell. Commonly used element types are triangular, quadrilateral, tetrahedral, and hexahedral. The number and quality of grid cells have a direct impact on the accuracy and efficiency of numerical calculations. A good grid needs to obtain as high numerical calculation accuracy as possible with as small a grid scale and degrees of freedom as possible. In order to meet the simulation requirements of high-preci...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/13G06F30/15G06F30/23G06F111/10
CPCG06F17/13G06F30/15G06F30/23G06F2111/10
Inventor 肖周芳王汝伊徐岗
Owner HANGZHOU DIANZI UNIV
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