A high order boundary scheme to simulate complex moving rigid body under impingement of shock wave

Ziqiang CHENG, Shihao LIU, Yan JIANG, Jianfang LU, Mengping ZHANG, Shuhai ZHANG

doi:10.1007/s10483-021-2735-7

Applied Mathematics and Mechanics >

2021 , Vol. 42 >Issue 6: 841 - 854

DOI: https://doi.org/10.1007/s10483-021-2735-7

Articles

A high order boundary scheme to simulate complex moving rigid body under impingement of shock wave

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1. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China;
2. South China Research Center for Applied Mathematics and Interdisciplinary Studies, South China Normal University, Guangzhou 510631, China;
3. State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan Province, China

Received date: 2020-12-02

Revised date: 2021-03-15

Online published: 2021-05-21

Supported by

the National Natural Science Foundation of China (Nos. 11901555, 11901213, 11871448, and 11732016) and the National Numerical Windtunnel Project (No. NNW2019ZT4-B10)

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Abstract

In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff (ILW) procedure developed in the previous work (TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15), 6023-6036 (2011)), in which the authors only considered the translation of the rigid body, we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.

Key words： inverse Lax-Wendroff (ILW) procedure; complex moving boundary scheme; Cartesian mesh; high order accuracy; compressible inviscid shock wave

Cite this article

Ziqiang CHENG, Shihao LIU, Yan JIANG, Jianfang LU, Mengping ZHANG, Shuhai ZHANG . A high order boundary scheme to simulate complex moving rigid body under impingement of shock wave[J]. Applied Mathematics and Mechanics, 2021 , 42(6) : 841 -854 . DOI: 10.1007/s10483-021-2735-7

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