面向三维激波问题的装配方法

邹东阳; 林敬周; 黄洁; 刘君

doi:10.7527/S1000-6893.2020.24141

航空学报 >

2021 , Vol. 42 >Issue 3: 124141 - 124141

DOI: https://doi.org/10.7527/S1000-6893.2020.24141

流体力学与飞行力学

面向三维激波问题的装配方法

邹东阳 ,
林敬周 ,
黄洁 ,
刘君

展开

1. 中国空气动力研究与发展中心超高速空气动力研究所, 绵阳 621000;
2. 大连理工大学航空航天学院, 大连 116024

收稿日期: 2020-04-27

修回日期: 2020-07-13

网络出版日期: 2020-08-03

收起

Fitting algorithms for three dimensional flows with shock waves

ZOU Dongyang ,
LIN Jingzhou ,
HUANG Jie ,
LIU Jun

Expand

1. Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China;
2. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China

Received date: 2020-04-27

Revised date: 2020-07-13

Online published: 2020-08-03

Fold

摘要

给出了一种基于非结构动网格技术的三维激波装配方法。在该方法中，三维激波面由被标记为激波属性的网格点连接构成，标记为激波属性的网格点称为激波点。激波点具有两组参数分别代表激波的上下游，利用激波点上下游参数求解R-H关系式获得激波点运动速度。非结构动网格技术的使用允许激波大幅度运动，降低了对初始激波位置的要求。通过引入网格属性定义避免了对计算网格进行分区，增加了装配激波的灵活性。通过球柱体绕流问题验证了该三维装配方法的合理性，针对三维激波装配中比较困难的交点装配问题，通过对三维激波反射以及三维激波相交等算例进行研究找到了可用的三维激波交点运动速度的确定方法，保证了激波运动过程中交点运动与流场求解之间的相容性，获得了相应的装配结果。

关键词： 三维激波装配; 三维激波相交; 非结构动网格; 有限体积法; 超声速流动

本文引用格式

邹东阳 , 林敬周 , 黄洁 , 刘君 . 面向三维激波问题的装配方法[J]. 航空学报, 2021 , 42(3) : 124141 -124141 . DOI: 10.7527/S1000-6893.2020.24141

Abstract

A three dimensional shock-fitting technique based on unstructured dynamic grids is proposed in this work. In this algorithm, the shock front comprises a series of grid nodes labeled as shock points which have two states, with one representing the upstream of the shock wave and the other the downstream. The R-H relations are solved using these two states on a shock point to obtain the velocity of the shock point. The use of unstructured dynamic grids enables the shock front to move in a large range, decreasing the requirement of the initial shock position. The shocks are labeled by the definition of grid nodes rather than using internal boundaries between different subdomains to improve the flexibility of fitting shock waves. The reliability of the proposed algorithm is proven by a test case of hypersonic flow past a hemisphere-cylinder, followed by the study of three-dimensional shock reflection and shock-shock interactions to solve the relatively complex shock interaction problems in three dimensional shock-fitting. To guarantee the compatibility of the shock point motion and the flow field, usable methods to determine the velocity of three dimensional shock interaction points are obtained, therefore ensuring the achievement of convergence shock-fitting results by this shock-fitting technique.

Key words： three dimensional shock-fitting; three dimensional shock interactions; unstructured dynamic grids; finite volume methods; supersonic flows

参考文献

[1] 童秉纲, 孔祥言, 邓国华. 气体动力学[M]. 北京:高等教育出版社, 2011:86-169. TONG B G, KONG X Y, DENG G H. Gas dynamics[M]. Beijing:Higher Education Press, 2011:86-169(in Chinese).
[2] 吴子牛, 白晨媛, 李娟, 等. 高超声速飞行器流动特征分析[J]. 航空学报, 2014, 36(1):58-85. WU Z N, BAI C J, et al. Analysis of flow characteristics for hypersonic vehicle[J]. Acta Aeronautica et Astonautica Sinica, 2014, 36(1):58-85(in Chinese).
[3] RICHTMYER R D, MORTON K W. Difference methods for initial-value problems[M]. New York:Interscience, 1958:90-230.
[4] HARTEN A. High resolution schemes for hyperbolic conservation law[J]. Journal of Computational Physics, 1983, 49:357-393.
[5] YEE H C, KLOPFER G H, MONTAGNE J L. High resolution shock-capturing schemes for inviscid and viscous hypersonic flows[J]. Journal of Computational Physics, 1990, 88:31-61.
[6] HARTEN A, ENGQUIST B, OSHER S, et al. Uniformly high order essentially non-oscillatory schemes[J]. Journal of Computational Physics, 1987, 71:231-303.
[7] LIU X D, OHSER S, CHAN T. Weighted essentially non-oscillatory schemes[J]. Journal of Computational Physics, 1994, 115:217-237.
[8] 张涵信. 无震荡无自由参数耗散差分格式[J]. 空气动力学学报, 1988, 2:143-165. ZHANG H X. Non-oscillatory and non-free-parameter dissipation difference scheme[J]. Acta Aerodynamics Sinica, 1988, 2:143-165(in Chinese).
[9] SALAS M D. A shock-fitting primer[M]. New York:CRC Press, 2009:33-34.
[10] LEE T K, ZHONG X L. Spurious numerical oscillations in simulation of supersonic flow using shock-capturing schemes[J]. AIAA Journal, 1999, 37:383-394.
[11] MORETTI G. Thirty-six years of shock-fitting[J]. Computer & Fluids, 2002, 31:719-723.
[12] PARPIA I H, PARIKH P. A solution-adaptive mesh generation method with cell-face orientation control[C]//Aerospace Sciences Meeting and Exhibit,1994-416, 1994:1-13.
[13] ROSENDALE J V. Floating shock fitting via Lagrangian adaptive meshes:Report No. 94-89[R]. Hampton, VA:NASA Langley Research Center,1994.
[14] TREPANIER J Y,REGGIO M,CAMARERO R, et al. A conservative shock fitting method on unstructured grids[J]. Journal of Computational Physics, 1996, 126(2):421-433.
[15] ZAHR M J, PERSSON P O. An optimization based discontinuous Galerkin approach for high-order accurate shock tracking[C]//AIAA SciTech Forum. Reston:AIAA, 2018:1-11.
[16] ZAHR M J, PERSSON P O. An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions[J]. Journal of Computational Physics, 2018, 365:105-134.
[17] MIRHOSEINI M, PERSSON P O, ZAHR M J. A full space solver for optimization-based, high-order shock tracking using a discontinuous Galerkin discretization[C]//AIAA SciTech Forum. Reston:AIAA, 2019:1-9.
[18] CORRIGAN A, KERCHER A D, KESSLER D A. A moving discontinuous Galerkin finite element method for flows with interfaces[J]. International Journal for Numerical Methods in Fluids, 2019, 89:362-406.
[19] CORRIGAN A T, KERCHER A D, KESSLER D A, et al. Application of the moving discontinuous Galerkin method with interface condition enforcement to shocked compressible flows[C]//AIAA AVIATION Forum. Reston:AIAA, 2018:1-10.
[20] CORRIGAN A T, KERCHER A D, KESSLER D A. The moving discontinuous Galerkin method with interface condition enforcement for unsteady three-dimensional flows[C]//AIAA SciTech Forum. Reston:AIAA, 2019:1-13.
[21] PACIORRI R, BONFIGLIOLI A. A shock-fitting technique for 2D unstructured grids[J]. Computers & Fluids, 2009, 38:715-726.
[22] BONFIGLIOLI A, PACIORRI R. Convergence analysis of shock-capturing and shock-fitting solutions on unstructured grids[J]. AIAA Journal, 2014, 52(7):1404-1416.
[23] PACIORRI R, BONFIGLIOLI A. Shock interaction computations on unstructured, two-dimensional grids using a shock-fitting technique[J]. Journal of Computational Physics, 2011, 230:3155-3177.
[24] 邹东阳, 刘君, 邹丽. 可压缩流动激波装配在格心型有限体积中的应用[J]. 航空学报, 2017, 38(12):121363. ZOU D Y, LIU J, ZOU L. Applications of the shock-fitting technique for compressible flow in cell-centered finite volume methods[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(12):121363(in Chinese).
[25] ZOU D Y, XU C G, DONG H B, et al. A shock-fitting technique for cell-centered finite volume methods on unstructured dynamic meshes[J]. Journal of Computational Physics, 2017, 345:866-882.
[26] 刘君, 邹东阳, 徐春光. 基于非结构动网格的非定常激波装配方法[J]. 空气动力学学报, 2015, 1:10-16. LIU J, ZOU D Y, XU C G. An unsteady shock-fitting technique based on unstructured moving grids[J]. Acta Aerodynamics Sinica, 2015, 1:10-16(in Chinese).
[27] 刘君, 邹东阳, 董海波. 动态间断装配法模拟激波壁面反射[J]. 航空学报, 2016, 37(3):836-846. LIU J, ZOU D Y, DONG H B. A moving discontinuity fitting technique to simulate shock waves impinged on a straight wall[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(3):836-846(in Chinese).
[28] 常思源, 白晓征, 崔小强, 等. 一种改进的非定常激波装配方法[J]. 航空学报, 2020, 41(2):123498. CHANG S Y, BAI X Z, CUI X Q, et al. An improved unsteady shock-fitting algorithm[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(2) 123498(in Chinese).
[29] 刘君, 陈洁, 韩芳. 基于离散等价方程的非结构网格有限差分法[J]. 航空学报, 2020, 41(1):123248. LIU J, CHEN J, HAN F. Finite difference method for unstructured grid based on discrete equivalent equation[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(1):123248(in Chinese).
[30] BONFIGLIOLI A, GROTTADAUREA M, PACIORRI R, et al. An unstructured, three-dimensional, shock-fitting solver for hypersonic flows[J]. Computers & Fluids, 2013,73:162-174.
[31] 刘君, 徐春光, 白晓征. 有限体积法和非结构动网格[M]. 北京:科学出版社, 2016:42-163. LIU J, XU C G, BAI X Z. Finite volume methods and unstructured dynamic grids technique[M]. Beijing:Science Press, 2016:42-163(in Chinese).
[32] HOUMTMAN E M, BANNINK W J, TIMMERMAN B H. Experimental and numerical investigation of the high-supersonic flow around an axi-symmetric blunt cylinder-flare model[C]//Proceedings of the 2nd European Symposium on Aerothermodynamics for Space Vehicles, 1995:517-522.

Options

文章导航

模态框（Modal）标题

摘要

本文引用格式

Abstract

参考文献