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The high speed flow problems usually involve complex flow phenomena, such as strong shock waves, shock-shock interactions, and shear layers. Prediction of these problems requires robust, efficient and accurate numerical methods. A robust flux splitting method capable of capturing crisp shock profile and exact contact surface is presented. Here, the flux vector of the Euler equation is split into convective and pressure parts according to the Toro's formulation. The accuracy of the numerical method at the contact discontinuity is examined first. Sufficient conditions of shock stability for this new method are obtained through a linear perturbation analysis. Several carefully chosen test problems are numerically investigated, and the numerical results demonstrate the accuracy and robustness of the proposed scheme.
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Keywords:
- hypersonic /
- shock capturing /
- contact discontinuity /
- shock instability
[1] Tchuen G, Fogang F, Burtschell Y, Woafo P 2014 Comput. Phys. Commun. 185 479
[2] Quan P C, Yi S H, Wu Y, Zhu Y Z, Chen Z 2014 Acta Phys. Sin. 63 084703 (in Chinese) [全鹏程, 易仕和, 武宇, 朱杨柱, 陈植 2014 63 084703]
[3] Wu Y, Yi S H, Chen Z, Zhang Q H, Gang D D 2013 Acta Phys. Sin. 62 184702 (in Chinese) [武宇, 易仕和, 陈植, 张庆虎, 冈敦殿 2013 62 184702]
[4] Zingg D W, Rango S D, Nemec M, Pulliam T H 2000 J. Comput. Phys. 160 683
[5] Fu Z, Liu K X, Luo N 2014 Chin. Phys. B 23 020202
[6] Park S H, Kwon J H 2003 J. Comput. Phys. 188 524
[7] Huang K B, Wu H, Yu H, Yan D 2011 Int. J. Numer. Methods Fluids 65 1026
[8] Pandolfi M, D' Ambrosio D 2001 J. Comput. Phys. 166 271
[9] Toro E F, Vázquez-Cendón M E 2012 Comput. Fluids 70 1
[10] Liou M S, Steffen C J 1993 J. Comput. Phys. 107 23
[11] Liou M S 1996 J. Comput. Phys. 129 364
[12] Liou M S 2006 J. Comput. Phys. 214 137
[13] Zha G C, Shen Y Q, Wang B Y 2011 Comput. Fluids 48 214
[14] Zha G C 2005 AIAA J. 43 1137
[15] Zha G C, Hu Z 2004 AIAA J. 42 205
[16] Zha G C, Bilgen E 1993 Int. J. Numer. Methods Fluids 17 115
[17] Mandal J C, Panwar V 2012 Comput. Fluids 63 148
[18] Sha S, Chen Z H, Xue D W 2013 Acta Phys. Sin. 62 144701 (in Chinese) [沙莎, 陈志华, 薛大文 2013 62 144701]
[19] Kitamura K, Shima E, Roe P L 2012 AIAA J. 50 2655
[20] Liou M S 2000 J. Comput. Phys. 160 623
[21] Xu K, Li Z W 2001 Int. J. Numer. Methods Fluids 37 1
[22] Quirk J J 1994 Int. J. Numer. Methods Fluids 18 555
[23] Henderson S J, Menart J A 2007 39th AIAA Thermophysics Conference Miami, America June 25-28 2007 p3904
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[1] Tchuen G, Fogang F, Burtschell Y, Woafo P 2014 Comput. Phys. Commun. 185 479
[2] Quan P C, Yi S H, Wu Y, Zhu Y Z, Chen Z 2014 Acta Phys. Sin. 63 084703 (in Chinese) [全鹏程, 易仕和, 武宇, 朱杨柱, 陈植 2014 63 084703]
[3] Wu Y, Yi S H, Chen Z, Zhang Q H, Gang D D 2013 Acta Phys. Sin. 62 184702 (in Chinese) [武宇, 易仕和, 陈植, 张庆虎, 冈敦殿 2013 62 184702]
[4] Zingg D W, Rango S D, Nemec M, Pulliam T H 2000 J. Comput. Phys. 160 683
[5] Fu Z, Liu K X, Luo N 2014 Chin. Phys. B 23 020202
[6] Park S H, Kwon J H 2003 J. Comput. Phys. 188 524
[7] Huang K B, Wu H, Yu H, Yan D 2011 Int. J. Numer. Methods Fluids 65 1026
[8] Pandolfi M, D' Ambrosio D 2001 J. Comput. Phys. 166 271
[9] Toro E F, Vázquez-Cendón M E 2012 Comput. Fluids 70 1
[10] Liou M S, Steffen C J 1993 J. Comput. Phys. 107 23
[11] Liou M S 1996 J. Comput. Phys. 129 364
[12] Liou M S 2006 J. Comput. Phys. 214 137
[13] Zha G C, Shen Y Q, Wang B Y 2011 Comput. Fluids 48 214
[14] Zha G C 2005 AIAA J. 43 1137
[15] Zha G C, Hu Z 2004 AIAA J. 42 205
[16] Zha G C, Bilgen E 1993 Int. J. Numer. Methods Fluids 17 115
[17] Mandal J C, Panwar V 2012 Comput. Fluids 63 148
[18] Sha S, Chen Z H, Xue D W 2013 Acta Phys. Sin. 62 144701 (in Chinese) [沙莎, 陈志华, 薛大文 2013 62 144701]
[19] Kitamura K, Shima E, Roe P L 2012 AIAA J. 50 2655
[20] Liou M S 2000 J. Comput. Phys. 160 623
[21] Xu K, Li Z W 2001 Int. J. Numer. Methods Fluids 37 1
[22] Quirk J J 1994 Int. J. Numer. Methods Fluids 18 555
[23] Henderson S J, Menart J A 2007 39th AIAA Thermophysics Conference Miami, America June 25-28 2007 p3904
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