基于离散等价方程的滑移壁面边界约束算法

魏雁昕; 刘君

doi:10.7638/kqdlxxb-2023.0018

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基于离散等价方程的滑移壁面边界约束算法

研究论文 | 更新时间：2026-05-28

- 基于离散等价方程的滑移壁面边界约束算法
- A constrained slip-wall boundary condition based on discrete equivalent equations
- 空气动力学学报 2023年41卷第12期页码：1-15
- 作者机构：
- 作者简介：
  
  魏雁昕（1990—），陕西宝鸡人，博士研究生，研究方向：计算空气动力学. E-mail：wei_yanxin@163.com
  刘君*，教授，研究方向：高超声速空气动力学，计算空气动力学. E-mail：liujun65@dlut.edu.com
- 基金信息：
  
  国家自然科学基金（11872144）
- DOI：10.7638/kqdlxxb-2023.0018
  中图分类号： V211.3
- 纸质出版：2023
- 稿件说明：
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魏雁昕, 刘君. 基于离散等价方程的滑移壁面边界约束算法[J]. 空气动力学学报, 2023, 41(12): 1−15.

WEI Yanxin, LIU Jun. A constrained slip-wall boundary condition based on discrete equivalent equations[J]. 2023, 41(12): 1-15.
魏雁昕, 刘君. 基于离散等价方程的滑移壁面边界约束算法[J]. 空气动力学学报, 2023, 41(12): 1−15. DOI： 10.7638/kqdlxxb-2023.0018

WEI Yanxin, LIU Jun. A constrained slip-wall boundary condition based on discrete equivalent equations[J]. 2023, 41(12): 1-15. DOI： 10.7638/kqdlxxb-2023.0018.

摘要

针对有限差分法的弯曲滑移壁面边界求解，以可以消除坐标变换诱导误差的离散等价方程为基础，提出一种利用虚拟节点赋值的边界约束算法。该方法利用无黏流动中壁面仅存在法向速度且恒等于零的约束条件，建立了法向动量通量为零的约束方程，通过求解约束方程确定虚拟节点的物理量，进而在边界节点实现通量计算。新方法在虚拟节点构造过程中将壁面当作流线处理，考虑了边界切向相邻节点对虚拟节点参数的影响，因此可以更为准确地求解包含曲率的物面边界。该方法在边界处和流场内部节点使用相同离散格式，在边界附近不存在格式相容性问题。相较于传统的使用虚拟节点的弱边界条件，该方法提高了虚拟节点参数的合理性，在时间推进过程中边界节点数值解可以严格满足无穿透条件。通过典型算例测试表明：本文所提方法适用于MUSCL格式和WENO格式，可以有效降低近边界区域的计算误差。

Abstract

To accurately solve the curved slip wall using finite difference methods

this work proposes a boundary constraint algorithm assigning ghost nodes based on discrete equivalents equation that eliminates the coordinate transformation-induced errors. Except for the wall-normal velocity

this method further constrains the wall-normal momentum flux at the wall to zero. The fluxes at the boundary nodes are determined by the physical quantities of ghost nodes by solving the constraint equation. The new method constructs ghost nodes by considering the wall as a streamline and takes the influence of neighboring wall tangential nodes into account

a more reasonable strategy than the traditional weak boundary condition. By doing so

the same discrete scheme can be used through the whole domain

avoiding the scheme compatibility issue near the wall so that the near-wall flow fields can be solved more accurately with the non-penetration wall condition strictly satisfied during time advancement. Typical examples demonstrate that the proposed method

which can be easily integrated into MUSCL and WENO schemes

can effectively reduce the numerical errors in the near-wall region.

关键词

Keywords

references

Gustafsson B, Kreiss H-O. Boundary conditions for time dependent problems with an artificial boundary[J]. Journal of Computational Physics, 1979, 30(3): 333-351. DOI: 10.1016/0021-9991(79)90119-0

YEE H C, BEAM R M, WARMING R F. Boundary approximations for implicit schemes for one-dimensional inviscid equations of gasdynamics[J]. AIAA Journal, 1982, 20(9): 1203-1211. DOI: 10.2514/3.51181

CHAKRAVARTHY S R. Euler equations - Implicit schemes and boundary conditions[J]. AIAA Journal, 1983, 21(5): 699-706. DOI: 10.2514/3.8136

DEMETRIOU SPARIS P. Second-order accurate boundary conditions for compressible flows[J]. AIAA Journal, 1984, 22(9): 1222-1228. DOI: 10.2514/3.48560

阎超. 计算流体力学方法及应用[M]. 北京: 北京航空航天大学出版社, 2006.

MENGALDO G, DE GRAZIA D, WITHERDEN F, et al. A guide to the implementation of boundary conditions in compact high-order methods for compressible aerodynamics[C]// 7th AIAA Theoretical Fluid Mechanics Conference, Atlanta, GA, 2014. doi: 10.2514/6.2014-2923

刘巍, 张理论, 王勇献. 计算空气动力学并行编程基础[M]. 北京: 国防工业出版社, 2013.

SUN Z S, REN Y X, ZHA B L, et al. High order boundary conditions for high order finite difference schemes on curvilinear coordinates solving compressible flows[J]. Journal of Scientific Computing, 2015, 65(2): 790-820. DOI: 10.1007/s10915-015-9988-4

ANDERSON J D. Computational fluid dynamics: The basics with applications[M]. New York: McGraw-Hill, 1995

DADONE A, GROSSMAN B. Surface boundary conditions for the numerical solution of the Euler equations[J]. AIAA Journal, 1994, 32(2): 285-293. DOI: 10.2514/3.11983

WANG Z J, SUN Y Z. Curvature-based wall boundary condition for the Euler equations on unstructured grids[J]. AIAA Journal, 2003, 41(1): 27-33. DOI: 10.2514/2.1931

R, KANNAN, . Curvature and entropy based wall boundary condition for the high order spectral volume Euler solver[J]. Computers Fluids, 2011, 44(1): 79-88. DOI: 10.1016/j.compfluid.2010.12.013

LIU J M, ZHAO N, HU O. The ghost cell method and its applications for inviscid compressible flow on adaptive tree cartesian grids[J]. Advances in Applied Mathematics and Mechanics, 2019, 1(5): 664-682. DOI: 10.4208/aamm.09-m0912

LIU J M. The study on adaptive Cartesian grid methods for compressible flow and their applications[D]. Leicester, East Midlands, UK: De Montfort University, 2014.

LI H. Numerical study of shock-associated noise in axisymmetric supersonic jet[D]. Mianyang: China Aerodynamics Research and Development Center, 2016 (in Chinese).

LIU J, WEI Y X, HAN F. Coordinate transformation induced errors of finite difference method[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(6): 124397.

LIU J, HAN F. Body-fitted coordinate transformation for finite difference method[J]. Physics of Gases, 2018, 3(5)18-29 (in Chinese). DOI: 10.19527/j.cnki.2096-1642.2018.05.003

LIU J, HAN F, XIA B. Mechanism and algorithm for geometric conservation law in finite difference method[J]. Acta Aerodynamica Sinica, 2018, 36(6): 917-926 (in Chinese).

LIU J, HAN F, WEI Y X. Numerical errors of high-order WENO schemes under specific conditions[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(2): 124940 (in Chinese).

HAN F, XU C G, LIU J. Improvement to a general methodology for free-stream preservation on curvilinear grids[J]. Physics of Fluids, 2022, 34(11): 116111. DOI: 10.1063/5.0120313

FRANKE R. Scattered data interpolation: tests of some methods[J]. Mathematics of Computation, 1982, 38(157): 181-200. DOI: 10.1090/s0025-5718-1982-0637296-4

TAN S R, SHU C W. Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws[J]. Journal of Computational Physics, 2010, 229(21): 8144-8166. DOI: 10.1016/j.jcp.2010.07.014

Borges R, Carmona M, Costa B, et al. An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws[J]. Journal of Computational Physics, 2008, 227(6): 3191-3211. DOI: 10.1016/j.jcp.2007.11.038

HARTEN A, LAX P D, VAN LEER B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws[J]. SIAM Review, 1983, 25(1): 35-61. DOI: 10.1137/1025002

SHU C W, OSHER S. Efficient implementation of essentially non-oscillatory shock-capturing schemes[J]. Journal of Computational Physics, 1989, 77(2): 439-471. DOI: 10.1016/0021-9991(88)90177-5

WANG Z J, FIDKOWSKI K, ABGRALL R, et al. High-order CFD methods: current status and perspective[J]. International Journal for Numerical Methods in Fluids, 2013, 72(8): 811-845. DOI: 10.1002/fld.3767

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