一种修正的Osher通量在高阶WCNS中的特性

doi:10.7527/S1000-6893.2016.0241

Abstract

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

CLC Number:

V211
O355

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.

References

[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.

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

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Shouchao HU, Yu ZHUANG, Xian LI, Tao JIANG. Hypersonic aero-heating environment research model HyHERM-I: Experiment [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(S2): 233-248.
[2]	GAO Huamin, ZHANG Zhuoran, WANG Chen, XUE Han, LIU Ye. Comparison and analysis of new high power density axial flux permanent magnet machine for electric propulsion aircraft [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 325229-325229.
[3]	LI Qiang, WAN Bingbing, YANG Kai, ZHU Tao. Experimental research on characteristics of pressure and heat flux fluctuation in hypersonic cone boundary layer [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(2): 124956-124956.
[4]	WANG Zhaoli, ZENG Tao, ZHOU Zhihong, CHEN Yu. Application of TVD scheme in numerical simulation of water droplet field [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(12): 627010-627010.
[5]	SHA Yundong, AI Size, ZHAO Fengtong, JIANG Zhuoqun, ZHANG Jiaming. Vibro-acoustic response analysis and fatigue life prediction of thin-walled structures with high speed heat flux [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(2): 223327-223327.
[6]	DING Mingsong, LIU Qingzong, JIANG Tao, GAO Tiesuo, DONG Weizhong, FU Yang'aoxiao. Impact of high temperature gas effect on hypersonic magnetohydrodynamic control [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(2): 123278-123278.
[7]	ZHU Yandan, WEI Dong, LIU Shenshen, ZENG Lei, GUI Yewei. Power optimization of non-uniform aerodynamic heating simulated by quartz lamp array [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(6): 122761-122761.
[8]	CHEN Dawei, ZHU Huiren, LI Huatai, LIU Haiyong, ZHOU Daoen. Effect of unsteady wake on full coverage film cooling effectiveness for a turbine blade [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(3): 122651-122651.
[9]	ZENG Lei, QIU Bo, LI Yu, WANG Anling, GUI Yewei. Influence of sensor surface temperature on heat flux measurement [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(6): 121940-121940.
[10]	LIU Julong, ZHANG Bi, BAI Qian, CHENG Bo. Temperature prediction of tool/workpiece contact zone in titanium milling [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(12): 422128-422128.
[11]	LIU Jingyuan. Extension of field synergy principle for convective heat transfer to high speed compressible boundary-layer flows [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(1): 121429-121429.
[12]	ZHUANG Shenglun, HUANG Wenxin, BU Feifei, SONG Ling. Low carrier ratio control of dual-stator winding induction generator for variable frequency AC system [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(12): 321242-321242.
[13]	YU Shiyi, HAO Zhenyang. Fault-tolerant internal permanent magnet generation system used in aviation engines [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(9): 2775-2787.
[14]	QIU Bo, GUO Yijun, ZHANG Haoyuan, ZENG Lei, SHI Youan, GUI Yewei. Free stream parameters' effects on vortexes and aerodynamic heating environment in thermal protection tile transverse gaps [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(3): 761-770.
[15]	YAN Zhenguo, LIU Huayong, MAO Meiliang, MA Yankai, ZHU Huajun. Development of 3rd-order HWCNS and its application in hypersonic flow [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(5): 1460-1470.