A constrained slip-wall boundary condition based on discrete equivalent equations

WEI Yanxin; LIU Jun

doi:10.7638/kqdlxxb-2023.0018

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A constrained slip-wall boundary condition based on discrete equivalent equations

更新时间：2026-05-28

- A constrained slip-wall boundary condition based on discrete equivalent equations
- Vol. 41, Issue 12, Pages: 1-15(2023)
- 作者机构：
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2023.0018
  CLC： V211.3
- Published：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.

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references

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