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Magnetohydrodynamic (MHD) equations are solved by using the CTU+CT (corner transport upwind + constrained transport) algorithm which guarantees the divergence-free constraint on the magnetic field. The interactions between shock wave and heavy or light triangular cylinder are investigated in detail in the cases with and without magnetic field. In the cases of hydrodynamic (B=0 T) and MHD (B=0.01 T), the numerical results indicate that heavy and light triangular cylinders have quite different wave patterns and jet structures after being impacted by a planar incident shock wave. Specifically, a regular refraction and downstream R22 jet are formed in the heavy case, whereas an irregular refraction and upstream air jet are generated in the light case. In the hydrodynamic case, the Richtmyer-Meshkov (R-M) instability and Kelvin-Helmholtz (K-H) instability are induced by the incident shock wave. Hereafter, both heavy and light density interfaces begin to roll up with a series of interfacial vortex sequences. In addition, a main vortex ring is formed in the heavy case, while a vortex dipole passing through the downstream interface is generated in the light case. In the MHD case, both heavy and light density interfaces remain smooth and interfacial vortex sequences vanish. Furthermore, the main vortex ring formed in the heavy cases and the vortex dipole generated in the light cases disappear. Moreover, in the presence of a magnetic field, a detailed investigation demonstrates that Lorentz forces give rise to the transport of baroclinic vorticities to the Alfvn waves. As a consequence, the deposition of interfacial vorticities decreases and the rolling-up of interfaces is suppressed. In the end, the vorticities are transformed into two vortex sheets travelling away from the density interfaces, and the R-M instability and K-H instability are well controlled. The quantitative investigations reveal that for both heavy and light triangular cylinders, magnetic field can accelerate the upstream interface and decelerate the downstream interface, especially for the light triangular cylinder.
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Keywords:
- magnetohydrodynamic /
- triangular cylinders /
- R-M instability /
- Alfvn wave
[1] Brouillette M 2002 Annu. Rev. Fluid Mech. 34 445
[2] Lindl J, Landen O, Edwards J, Moses E 2014 Phys. Plasmas 21 339
[3] Sano T, Nishihara K, Matsuoka C, Inoue T 2012 ApJ. 758 12
[4] Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297
[5] Meshkov E E 1969 Fluid Dyn. 4 101
[6] Rudinger G, Somers L M 1960 J. Fluid Mech. 7 161
[7] Haas J F, Sturtevant B 1987 J. Fluid Mech. 181 41
[8] Layes G, Jourdan G, Houas L 2003 Phys. Rev. Lett. 91 174502
[9] Layes G, Jourdan G, Houas L 2009 Phys. Fluids 21 074102
[10] Ranjan D, Oakley J, Bonazza R 2011 Annu Rev. Fluid Mech. 43 117
[11] Ranjan D, Niederhaus J H J, Oakley J G, Anderson M H 2008 Phys. Fluids 20 24
[12] Zhai Z G, Wang M H, Si T, Luo X S 2014 J. Fluid Mech. 757 800
[13] Luo X S, Wang M H, Si T, Zhai Z G 2015 J. Fluid Mech. 773 366
[14] Dong P, Si T, Zhai Z G 2016 J. Fluid Mech. 802 186
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[16] Sha S, Chen Z H, Xue D W, Zhang H 2014 Acta Phys. Sin. 63 085205 (in Chinese)[沙莎, 陈志华, 薛大文, 张辉 2014 物理学报 63 085205]
[17] Sha S, Chen Z H, Zhang Q B 2015 Acta Phys. Sin. 64 015201 (in Chinese)[沙莎, 陈志华, 张庆兵 2015 物理学报 64 015201]
[18] Mininni P D 2010 Annu. Rev. Fluid Mech. 43 377
[19] Tao Y S, Wang L F, Ye W H, Zhang G C, Zhang J C, Li Y J 2012 Acta Phys. Sin. 61 075207 (in Chinese)[陶烨晟, 王立锋, 叶文华, 张广财, 张建成, 李英骏 2012 物理学报 61 075207]
[20] Li Y, Luo X S 2014 Acta Phys. Sin. 63 085230 (in Chinese)[李源, 罗喜胜 2014 物理学报 63 085230]
[21] Wu C C 2000 J. Geophys. Res-Space 105 7533
[22] Samtaney R 2003 Phys. Fluids 15 L53
[23] Wheatley V, Pullin D I, Samtaney R 2005 Phys. Rev. Lett. 95 125002
[24] Wheatley V, Samtaney R, Pullin D I 2009 Phys. Fluids 21 082102
[25] Wheatley V, Samtaney R, Pullin D I, Gehre R M 2014 Phys. Fluids 26 238
[26] Sano T, Inoue T, Nishihara K 2013 Phys. Rev. Lett. 111 20500
[27] Cao J T, Wu Z W, Ren H J, Dong L 2008 Phys. Plasmas 15 445
[28] Mostert W, Wheatley V, Samtaney R, Pullin D I 2015 Phys. Fluids 27 104102
[29] Lin Z Y, Zhang H H, Chen Z H, Liu Y, Hong Y J 2017 Int. J. Comput. Fluid D. 31 21
[30] Lin Z Y, Zhang H H, Chen Z H, Liu Y 2017 Explosion and Shock Waves 37 748 (in Chinese)[林震亚, 张焕好, 陈志华, 刘迎 2017 爆炸与冲击 37 748]
[31] Gardiner T A, Stone J M 2008 J. Comput. Phys. 227 4123
[32] Londrillo P, Zanna L D 2003 J. Comput. Phys. 195 17
[33] Qin J H, Jiang X H, Dong G D, Guo Z Q, Chen Z H 2018 Fluid Dyn. Res. 50 045508
[34] Henderson L F, Colella P, Puckett E G 2006 J. Fluid Mech. 224 1
[35] Landau L D, Lifshitz E M 1960 Electrodynamics of Continuous Media (Oxford: Pergamon) pp241-243
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[1] Brouillette M 2002 Annu. Rev. Fluid Mech. 34 445
[2] Lindl J, Landen O, Edwards J, Moses E 2014 Phys. Plasmas 21 339
[3] Sano T, Nishihara K, Matsuoka C, Inoue T 2012 ApJ. 758 12
[4] Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297
[5] Meshkov E E 1969 Fluid Dyn. 4 101
[6] Rudinger G, Somers L M 1960 J. Fluid Mech. 7 161
[7] Haas J F, Sturtevant B 1987 J. Fluid Mech. 181 41
[8] Layes G, Jourdan G, Houas L 2003 Phys. Rev. Lett. 91 174502
[9] Layes G, Jourdan G, Houas L 2009 Phys. Fluids 21 074102
[10] Ranjan D, Oakley J, Bonazza R 2011 Annu Rev. Fluid Mech. 43 117
[11] Ranjan D, Niederhaus J H J, Oakley J G, Anderson M H 2008 Phys. Fluids 20 24
[12] Zhai Z G, Wang M H, Si T, Luo X S 2014 J. Fluid Mech. 757 800
[13] Luo X S, Wang M H, Si T, Zhai Z G 2015 J. Fluid Mech. 773 366
[14] Dong P, Si T, Zhai Z G 2016 J. Fluid Mech. 802 186
[15] 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 物理学报 62 144701]
[16] Sha S, Chen Z H, Xue D W, Zhang H 2014 Acta Phys. Sin. 63 085205 (in Chinese)[沙莎, 陈志华, 薛大文, 张辉 2014 物理学报 63 085205]
[17] Sha S, Chen Z H, Zhang Q B 2015 Acta Phys. Sin. 64 015201 (in Chinese)[沙莎, 陈志华, 张庆兵 2015 物理学报 64 015201]
[18] Mininni P D 2010 Annu. Rev. Fluid Mech. 43 377
[19] Tao Y S, Wang L F, Ye W H, Zhang G C, Zhang J C, Li Y J 2012 Acta Phys. Sin. 61 075207 (in Chinese)[陶烨晟, 王立锋, 叶文华, 张广财, 张建成, 李英骏 2012 物理学报 61 075207]
[20] Li Y, Luo X S 2014 Acta Phys. Sin. 63 085230 (in Chinese)[李源, 罗喜胜 2014 物理学报 63 085230]
[21] Wu C C 2000 J. Geophys. Res-Space 105 7533
[22] Samtaney R 2003 Phys. Fluids 15 L53
[23] Wheatley V, Pullin D I, Samtaney R 2005 Phys. Rev. Lett. 95 125002
[24] Wheatley V, Samtaney R, Pullin D I 2009 Phys. Fluids 21 082102
[25] Wheatley V, Samtaney R, Pullin D I, Gehre R M 2014 Phys. Fluids 26 238
[26] Sano T, Inoue T, Nishihara K 2013 Phys. Rev. Lett. 111 20500
[27] Cao J T, Wu Z W, Ren H J, Dong L 2008 Phys. Plasmas 15 445
[28] Mostert W, Wheatley V, Samtaney R, Pullin D I 2015 Phys. Fluids 27 104102
[29] Lin Z Y, Zhang H H, Chen Z H, Liu Y, Hong Y J 2017 Int. J. Comput. Fluid D. 31 21
[30] Lin Z Y, Zhang H H, Chen Z H, Liu Y 2017 Explosion and Shock Waves 37 748 (in Chinese)[林震亚, 张焕好, 陈志华, 刘迎 2017 爆炸与冲击 37 748]
[31] Gardiner T A, Stone J M 2008 J. Comput. Phys. 227 4123
[32] Londrillo P, Zanna L D 2003 J. Comput. Phys. 195 17
[33] Qin J H, Jiang X H, Dong G D, Guo Z Q, Chen Z H 2018 Fluid Dyn. Res. 50 045508
[34] Henderson L F, Colella P, Puckett E G 2006 J. Fluid Mech. 224 1
[35] Landau L D, Lifshitz E M 1960 Electrodynamics of Continuous Media (Oxford: Pergamon) pp241-243
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