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When shock waves passes through a triangle wedge (Schardin's problem), some complicated physical phenomena, including shock wave Mach refection and diffraction, wedge wake, vortexlet, etc. may occur. In this paper, the Schardin's problem is investigated numerically with the combination of the third-order WENO scheme, structured adaptive mesh refinement (AMR) method and immersed boundary method. Our numerical results show clearly the interaction between the incident shock wave and the triangle wedge, the Mach reflection on the wedge surface, its diffraction at the wedge tips, and the induction of the main vortex, which accord excellently with Schardin's experimental and previous numerical results. In addition, our numerical results display in detail the induction process of the vortexlet along the slip layer of the main vortex and the interaction of the shock wave with the vortexlet, and the generation of the serial acoustic waves, which have not been reported in the literature.
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Keywords:
- shock waves /
- vortexlet /
- WENO scheme /
- AMR method
[1] Schardin H 1957 Photo Sci.5 19
[2] Sivier S,Loth E,Baum J,Lohner R 1992 Shock Waves 2 31
[3] Chang S M,Chang KS 2000 Shock Waves 10 333
[4] Uchiyama N,Inoue O 1995 AIAA J.33 1740
[5] Chen Z H,Fan B C,Zhou B M,Li H Z 2007 Chin.Phys.16 1077
[6] Liu X D,Osher S,Chan T 1994 Comput.Phys.115 200
[7] Berger M,Colella P 1988 Comput.Phys.82 64
[8] Kim J,Kim D,Choi H 2001 Comput.Phys.171 132
[9] Dadone A,Grossman B 2002 40th AIAA Aerospace Sciences Meeting & Exhibit Reno,USA,January 14-17,2002 p1059
[10] Huang J C,Hsieh T Y,Yang J Y,Takayama K 2008 Shock Waves 18 193
[11] Charendon S 1961 Hydrodynamic and Hydromagnetic Stability(Oxford:Clarendon press) p481
[12] Wang L F,Teng A P,Ye W H,Fan Z F,Tao Y M,Lin C D,Li Y J 2009 Acta Phys.Sin.58 8426 (in Chinese) [王立锋, 滕爱萍,叶文华, 范征锋, 陶烨晟, 林传栋, 李英骏 2009 物理学报 58 8426]
[13] Chang K S,Chang S M 2004 Symposium on Interdisciplinary Shock Wave Research (Japan:Sendai) p22
[14] Inoue O,Hattori Y 1999 J.Fluid Mech.380 81
[15] Grasso F,Pirozzoli S 2000 Theor.Comp.Fluid Dyn.13 421
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[1] Schardin H 1957 Photo Sci.5 19
[2] Sivier S,Loth E,Baum J,Lohner R 1992 Shock Waves 2 31
[3] Chang S M,Chang KS 2000 Shock Waves 10 333
[4] Uchiyama N,Inoue O 1995 AIAA J.33 1740
[5] Chen Z H,Fan B C,Zhou B M,Li H Z 2007 Chin.Phys.16 1077
[6] Liu X D,Osher S,Chan T 1994 Comput.Phys.115 200
[7] Berger M,Colella P 1988 Comput.Phys.82 64
[8] Kim J,Kim D,Choi H 2001 Comput.Phys.171 132
[9] Dadone A,Grossman B 2002 40th AIAA Aerospace Sciences Meeting & Exhibit Reno,USA,January 14-17,2002 p1059
[10] Huang J C,Hsieh T Y,Yang J Y,Takayama K 2008 Shock Waves 18 193
[11] Charendon S 1961 Hydrodynamic and Hydromagnetic Stability(Oxford:Clarendon press) p481
[12] Wang L F,Teng A P,Ye W H,Fan Z F,Tao Y M,Lin C D,Li Y J 2009 Acta Phys.Sin.58 8426 (in Chinese) [王立锋, 滕爱萍,叶文华, 范征锋, 陶烨晟, 林传栋, 李英骏 2009 物理学报 58 8426]
[13] Chang K S,Chang S M 2004 Symposium on Interdisciplinary Shock Wave Research (Japan:Sendai) p22
[14] Inoue O,Hattori Y 1999 J.Fluid Mech.380 81
[15] Grasso F,Pirozzoli S 2000 Theor.Comp.Fluid Dyn.13 421
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