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A Boundary Processing Technique of Weno Difference Method

A differential method and boundary processing technology, applied in electrical digital data processing, special data processing applications, instruments, etc., can solve problems such as lack of high-order numerical methods, processing boundaries without compactness, and inability to handle complex boundaries.

Active Publication Date: 2018-01-02
BEIHANG UNIV
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Problems solved by technology

However, under the conditions of the current computer scale and solving ability, the computational efficiency of the current mainstream numerical methods cannot meet the needs of this engineering practical application problem. One of the keys to solving this problem is to improve the efficiency of the flow field solver
[0003] At present, a variety of coupling methods have appeared to take full advantage of the advantages of popular high-precision numerical methods, such as WENO limiter discontinuous finite element method, high-order SV method, coupled DG / FV method, multi-region coupled DG and WENO method, in which the multi-area coupled DG and WENO methods have the advantages of high efficiency, high precision and easy handling of complex boundaries, but the most efficient of all current high-order methods is still the finite difference method, but this method generally needs to be in the structure The calculation is performed on the grid, and it cannot deal with complex boundaries, and there is no compactness when dealing with boundaries, so there is a lack of a high-order numerical method that can help the finite difference method to deal with complex boundaries compactly

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  • A Boundary Processing Technique of Weno Difference Method
  • A Boundary Processing Technique of Weno Difference Method
  • A Boundary Processing Technique of Weno Difference Method

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Embodiment Construction

[0023] First, we illustrate the main process of our algorithm for the one-dimensional scalar Burgers equation, such as figure 1 The area of ​​the first step is divided into two parts, in which the WENO-FD part on the left is the internal unit area, and the DG grid on the right is the boundary unit area.

[0024] The specific implementation process of WENO-FD in the internal area is as follows:

[0025] First, we do not consider flux splitting, assuming f'(u)>0, then in unit I i The conserved finite difference scheme is

[0026]

[0027] where u i (t)=u(x i ,t) is unit I i the point value at the midpoint, For the numerical flux can be expressed as

[0028]

[0029] Such as figure 2 Except for the two fluxes at the boundary of the internal unit, most of the internal unit fluxes we choose figure 2 The template S=(S 1 ,S 2 ,S 3 ), flux in Then It is obtained by Lagrangian interpolation of the value of the unit contained in each small template. For the 5rd...

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Abstract

The present invention provides a boundary processing technology for flow field calculation using WENO differential numerical method, which can achieve consistent high precision in flow field calculation, and can handle complex boundaries. The main technology of the invention is on the structural grid The points and steps are: (1) Mesh division, the grid is divided into two areas, the inner area and the boundary area, and the boundary area has only one layer of grid, so as to minimize the complicated calculation of the DG in the boundary area. (2) Spatial discretization, using the WENO finite difference method for spatial discretization of the internal area. (3) Boundary processing, using the DG method to discretize the space of the boundary area. (4) Coupling processing, which couples the boundary processing part with the internal area, and the boundary area provides derivative information through DG polynomial approximation. (5) Time discrete, display time discrete by TVD‑Runge‑Kutta method. (6) Post-processing, the flow field results are visually simulated by commercial software such as Tecplot or Paraview.

Description

technical field [0001] The invention relates to the field of computational fluid dynamics numerical methods, in particular to a boundary processing technology of a high-precision finite difference method for solving hyperbolic conservation law equations. Background technique [0002] Numerical simulation of three-dimensional complex flows of aircraft and related multi-objective optimization problems are currently hot frontier issues in computational fluid dynamics, and are also an application problem oriented to actual engineering needs. However, under the conditions of the current computer scale and solving ability, the computational efficiency of the current mainstream numerical methods cannot meet the needs of this engineering practical application problem. One of the keys to solving this problem is to improve the efficiency of the flow field solver . [0003] At present, a variety of coupling methods have appeared to take full advantage of the advantages of popular high...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/50
Inventor 刘铁钢王坤程剑
Owner BEIHANG UNIV
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