基于高阶间断伽辽金数值方法的浸没边界法

王婷婷; 吕宏强; 安慰

doi:10.7638/kqdlxxb-2022.0138

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基于高阶间断伽辽金数值方法的浸没边界法

研究论文 | 更新时间：2026-05-28

- 基于高阶间断伽辽金数值方法的浸没边界法
- Immersed boundary method based on high-order discontinuous Galerkin method
- 空气动力学学报 2023年41卷第9期页码：96-106
- 作者机构：
  
  南京航空航天大学航空学院,南京,210016
- 作者简介：
  
  王婷婷（1997-），女，浙江温州人，硕士研究生，研究方向：计算流体力学. E-mail：1090551007@qq.com
  吕宏强*，教授，研究方向：计算流体力学. E-mail：hongqiang.lu@nuaa.edu.cn
- 基金信息：
  
  气动噪声控制重点实验室基金（ANCL20190103）
- DOI：10.7638/kqdlxxb-2022.0138
  中图分类号： O357.1;V211.3
- 纸质出版：2023
- 稿件说明：
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王婷婷, 吕宏强, 安慰. 基于高阶间断伽辽金数值方法的浸没边界法[J]. 空气动力学学报, 2023, 41(9): 96−106.

WANG Tingting, LYU Hongqiang, AN Wei. Immersed boundary method based on high-order discontinuous Galerkin method[J]. 2023, 41(9): 96-106.
王婷婷, 吕宏强, 安慰. 基于高阶间断伽辽金数值方法的浸没边界法[J]. 空气动力学学报, 2023, 41(9): 96−106. DOI： 10.7638/kqdlxxb-2022.0138

WANG Tingting, LYU Hongqiang, AN Wei. Immersed boundary method based on high-order discontinuous Galerkin method[J]. 2023, 41(9): 96-106. DOI： 10.7638/kqdlxxb-2022.0138.

摘要

为了降低复杂边界条件下贴体网格生成难度，近年来基于笛卡尔网格的浸没边界法逐渐成为研究此类问题的主要数值方法之一，然而计算精度和计算效率仍然是此类方法目前面临的挑战。与传统的空间2阶精度的有限体积格式相比，空间精度为3阶或3阶以上的高精度方法具有空间精度高、数值分辨率高、数值耗散小的优点，而作为高精度数值方法之一的间断伽辽金方法在浸没边界方面的应用仍较少。本文将高阶间断伽辽金方法的高精度优势与浸没边界法无需贴体网格的优势结合起来，提出了适用于可压缩流动的高精度浸没边界法。其中边界条件采用体积惩罚方式实现，同时采用牛顿法迭代以及MPI并行提高计算效率，物面的数据重建采用插值点处的逆距离权重（IDW-IP）方法代替高阶格式下多项式插值方法。本文基于笛卡尔网格测试验证了二维定常和非定常情况下的数值模拟效果，并与传统贴体网格的计算结果进行了对比。

Abstract

To decrease the difficulty of generating body-fitted meshes for complex geometries

the immersed boundary (IB) method based on Cartesian mesh has gradually become a popular numerical method for studying such problems in recent years. However

accuracy and efficiency of this method still need to be improved. Compared with the traditional finite volume scheme with second-order spatial accuracy

third-order or higher-order numerical methods have the advantages of high spatial accuracy

high numerical resolution and low numerical dissipation. However

the discontinuous Galerkin (DG) method

as one of the high-precision numerical methods

is still rarely applied with the immersed boundary. This paper proposes a high-order discontinuous Galerkin method for compressible flows by combining the advantage of the high-order discontinuous Galerkin method and the immersed boundary method. The boundary conditions in this paper are realized by the volume penalization method. Newton’s method iteration and MPI are used to improve computational efficiency. The inverse distance weight at interpolation point (IDW-IP) instead of the high-order polynomial defined in each element to perform high-order data reconstruction at the object surface. Based on the Cartesian grids

numerical tests are performed for two-dimensional steady and unsteady flows

and comparisons with those on traditional body-fitted grids are given.

关键词

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