一种修正的Osher通量在高阶WCNS中的特性

doi:10.7527/S1000-6893.2016.0241

流体力学与飞行力学

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一种修正的Osher通量在高阶WCNS中的特性

朱华君¹, 燕振国¹, 刘化勇¹, 毛枚良^1,2

1. 中国空气动力研究与发展中心空气动力学国家重点实验室, 绵阳 621000;
2. 中国空气动力研究与发展中心计算空气动力研究所, 绵阳 621000

收稿日期:2016-06-17 修回日期:2016-08-25 出版日期:2017-05-15 发布日期:2016-09-26
通讯作者: 刘化勇 E-mail:hyliu@skla.cardc.cn
基金资助:
国家自然科学基金（11301525，11372342，11572342）

Properties of Osher flux with entropy fix in high-order WCNS

ZHU Huajun¹, YAN Zhenguo¹, LIU Huayong¹, MAO Meiliang^1,2

1. State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China;
2. China Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China

Received:2016-06-17 Revised:2016-08-25 Online:2017-05-15 Published:2016-09-26
Supported by:
National Natural Science Foundation of China (11301525,11372342 and 11572342)

摘要/Abstract

摘要：

将一种基于多维修正的Osher通量运用于高阶加权紧致非线性格式（WCNS）中，该修正通量主要在垂直于激波面的界面上增加耗散，能够改善Osher通量的激波捕捉稳定性，同时对边界层和接触间断的分辨率影响非常小。对修正的Osher通量在高阶WCNS中的特性进行研究，通过数值模拟测试了基于Osher通量的WCNS的激波稳定性、热流预测精度、边界层模拟能力、激波边界层干扰模拟能力，并与Steger-Warming通量和Roe通量进行了对比。结果表明修正后的Osher通量比Harten修正的Roe通量具有更好的激波捕捉鲁棒性，而边界层、驻点热流值和激波边界层干扰的模拟则明显优于Steger-Warming通量。上述结果说明了基于修正的Osher通量的高阶WCNS具有较好的激波捕捉特性、热流预测精度和边界层计算能力。

关键词: 通量, 高阶WCNS, 激波稳定性, 热流计算, 边界层计算

Abstract:

Osher flux with a multi-dimensional entropy fix is applied for high order weighted compact nonlinear scheme (WCNS). The entropy fix technique is used to mainly improve the dissipation on the interfaces perpendicular to the shock wave, and can thus improve shock wave stability and may not influence contact resolution. The properties of the Osher flux in high order WCNS schemes are studied. Numerical investigations are made to test properties of shock wave stability, accuracy of viscous heating computation, and boundary layer and shock boundary layer interaction calculation abilities. Comparisons with Steger-Warming flux and Roe flux are also made. Numerical results show that the Osher flux with entropy fix is more robust than Roe flux with Harten fix in shock capturing, and is better in viscous heating computation than Steger-Warming flux. These results illustrate that high order WCNS based on Osher flux with entropy fix is robust in caputuring shock waves, can get accurate heat flow prediction and has good simulation of the boundary layer.

Key words: flux, high order WCNS, shock wave stability, heat flow computation, boundary layer calculation

中图分类号:

V211
O355

朱华君, 燕振国, 刘化勇, 毛枚良. 一种修正的Osher通量在高阶WCNS中的特性[J]. 航空学报, 2017, 38(5): 120543-120543.

ZHU Huajun, YAN Zhenguo, LIU Huayong, MAO Meiliang. Properties of Osher flux with entropy fix in high-order WCNS[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(5): 120543-120543.

参考文献

[1] ENGQUIST B, OSHER S. Stable and entropy satisfying approximations for transonic flow calculations[J]. Mathematics of Computation, 1980, 34(149):45-57.
[2] ENGQUIST B, OSHER S. One sided difference approximation for nonlinear conservation laws[J]. Mathematics of Computation, 1981, 36(154):321-351.
[3] OSHER S, SOLOMON F. Upwind difference schemes for hyperbolic systems of conservation laws[J]. Mathematics of Computation, 1982, 38(158):339-374.
[4] OSHER S, CHAKRAVARTHY S. Upwind schemes and boundary conditions with application to Euler equations in general geometries[J]. Journal of Computational Physics, 1983, 50(3):447-481.
[5] CHAKRAVARTHY S, OSHER S. Numerical experiments with the Osher upwind scheme for the Euler equations[J]. AIAA Journal, 1983, 21(9):1241-1248.
[6] OSHER S. Riemann solvers, the entropy condition, and difference approximations[J]. SIAM Journal on Numerical Analysis, 1984, 21(2):217-235.
[7] OSHER S, CHAKRAVARTHY S. High resolution schemes and the entropy condition[J]. SIAM Journal on Numerical Analysis, 1984, 21(5):955-984.
[8] AMALADAS J R, KAMATH H. Accuracy assessment of upwind algorithms for steady-state computations[J]. Computers & Fluids, 1998, 27(8):941-962.
[9] SANDERS R, MORANO E, DRUGUET M. Multidimensional dissipation for upwind schemes:Stability and applications to gas dynamics[J]. Journal of Computational Physics, 1998, 145(2):511-537.
[10] PANDOLFI M, D'AMBROSIO D. Numerical instabilities in upwind methods:Analysis and cures for the "carbuncle" phenomenon[J]. Journal of Computational Physics, 2001, 166(2):271-301.
[11] REN Y X. A robust shock-capturing scheme based on rotated Riemann solvers[J]. Computers & Fluids, 2003, 32(10):1379-1403.
[12] ZHU H J, DENG X G, MAO M L, et al. Osher flux with entropy fix for two-dimensional Euler equations[J]. The Advances in Applied Mathematics and Mechanics, 2016, 8(4):670-692.
[13] DENG X G, MAO M L. Weighted compact high-order nonlinear schemes for the Euler equations:AIAA-1997-1941[R]. Reston:AIAA, 1997.
[14] DENG X G, MAO M L. New high-order hybrid cell-edge and cell-node weighted compact nonlinear schemes:AIAA-2011-3857[R]. Reston:AIAA, 2011.
[15] DENG X G, MAO M L, TU G H, et al. Geometric conservation law and applications to high-order finite difference schemes with stationary grids[J]. Journal of Computational Physics, 2011, 230(4):1100-1115.
[16] DENG X G, MIN Y B, MAO M L, et al. Further studies on geometric conservation law and applications to high-order finite difference schemes with stationary grids[J]. Journal of Computational Physics, 2013, 239:90-111.
[17] 燕振国, 刘化勇, 毛枚良, 等. 三阶HWCNS的构造及其在高超声速流动中的应用[J]. 航空学报, 2015, 36(5):1460-1470. YAN Z G, LIU H Y, MAO M L, et al. Development of 3rd-order HWCNS and its application in hypersonic flow[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(5):1460-1470 (in Chinese).
[18] 涂国华, 燕振国, 赵晓慧, 等. SA和SST湍流模型对高超声速边界层强制转捩的适应性[J]. 航空学报, 2015, 36(5):1471-1479. TU G H, YAN Z G, ZHAO X H, et al. SA and SST turbulence models for hypersonic forced boundary layer transition[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(5):1471-1479 (in Chinese).
[19] 燕振国, 刘化勇, 毛枚良, 等. 基于高阶耗散紧致格式的GMRES方法收敛特性研究[J]. 航空学报, 2014, 35(5):1181-1192. YAN Z G, LIU H Y, MAO M L, et al. Convergence property investigation of GMRES method based on high-order dissipative compact scheme[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(5):1181-1192 (in Chinese).
[20] DENG X G, ZHANG H X. Developing high-order weighted compact nonlinear schemes[J]. Journal of Computational Physics, 2000, 165(1):22-44.
[21] SHU C W, OSHER S. Efficient implementation of essentially non-oscillatory shock capturing schemes[J]. Journal of Computational Physics, 1988, 77(2):439-471.
[22] KITAMURA K, SHIMA E, NAKAMURA Y, et al. Evaluation of Euler fluxes for hypersonic heating computations[J]. AIAA Journal, 2010, 48(4):763-776.
[23] HARTEN A. On a class of high resolution total-variation-stable finite-difference schemes[J]. SIAM Journal of Numerical Analysis, 1984, 21(1):1-23.
[24] KITAMURA K. A further survey of shock capturing methods on hypersonic heating issues:AIAA-2013-2698[R]. Reston:AIAA, 2013.
[25] MA Y K, YAN Z G, ZHU H J. Improvement of multistep WENO scheme and its extension to higher orders of accuracy[J]. International Journal of Numerical Methods Fluids, 2016, 82(12):818-838.
[26] DELERY J M, PANARAS A G. Shock-wave/boundary-layer interactions in high-Mach-number flows:AGARD-AR-319[R]. 1996.
[27] MOSS J N, DOGRA V K, PRICE J M. DSMC simulations of viscous interactions for a hollow cylinder-flare configuration:AIAA-1994-2015[R]. Reston:AIAA, 1994.
[28] KIM K H, KIM C. Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows Part Ⅱ:Multi-dimensional limiting process[J]. Journal of Computational Physics, 2005, 208(2):570-615.

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一种修正的Osher通量在高阶WCNS中的特性

Properties of Osher flux with entropy fix in high-order WCNS

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