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In this paper we develop the Runge-Kutta discontinuous Galerkin finite element method for two-dimensional compressible gas dynamic equations in unified coordinate. The equations for fluid dynamics and geometry conservation laws are solved simultaneously. All the calculations can be performed on the fixed meshes. The information about the grid velocities is not needed in calculation. Some numerical examples are given to evaluate the efficiency and the reliability of the scheme. The numerical results show that the algorithm works well.
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Keywords:
- unified coordinate /
- Runge-Kutta discontinuous Galerkin finite element method /
- two-dimensional gas dynamic equations
[1] Hirt C, Amsden A, Cook J 1974 J. Comput. Phys. 14 227
[2] Jia Z P, Yu X J 2007 Chin. J. Comput. Phys. 24 543 (in Chinese) [贾祖朋, 蔚喜军 2007 计算物理 24 543]
[3] Hui W H, Li P Y, Li Z W 1999 J. Comput. Phys. 153 596
[4] Jia P Y 2006 Chin. J. Comput. Phys. 23 19 (in Chinese) [贾鹏彦 2006 计算物理 23 19]
[5] Cockburn B, Shu C W 1991 Math. Model. Numer. Anal. 25 337
[6] Cockburn B, Shu C W 1989 Math. Comp. 52 411
[7] Cockburn B, Lin S Y, Shu C W 1989 J. Comput. Phys. 84 90
[8] Cockburn B, Hou S, Shu C W 1990 Math. Comp. 54 545
[9] Cockburn B, Shu C W 1998 J. Comput. Phys. 141 199
[10] Cockburn B, Shu C W 2001 J. Sci. Comput. 16 173
[11] Chen D W, Yu X J 2009 Chin. J. Comput. Phys. 26 501 (in Chinese) [陈大伟, 蔚喜军 2009 计算物理 26 501]
[12] Zhang L, Yuan L 2010 Chin. J. Comput. Phys. 27 509 (in Chinese) [张磊, 袁礼 2010 计算物理 27 509]
[13] Jia Z P, Zhang S D 2011 J. Comput. Phys. 230 2496
[14] Maire P H, Abgrall R, Breil J, Ovadia J 2007 SIAM J. Sci. Comput. 29 1781
[15] Toro E F 1997 Riemann Solvers and Numerical Methods for Fluid Dynamics-a Practical Introduction (2nd Ed.) (Berlin: Springer) p581
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[1] Hirt C, Amsden A, Cook J 1974 J. Comput. Phys. 14 227
[2] Jia Z P, Yu X J 2007 Chin. J. Comput. Phys. 24 543 (in Chinese) [贾祖朋, 蔚喜军 2007 计算物理 24 543]
[3] Hui W H, Li P Y, Li Z W 1999 J. Comput. Phys. 153 596
[4] Jia P Y 2006 Chin. J. Comput. Phys. 23 19 (in Chinese) [贾鹏彦 2006 计算物理 23 19]
[5] Cockburn B, Shu C W 1991 Math. Model. Numer. Anal. 25 337
[6] Cockburn B, Shu C W 1989 Math. Comp. 52 411
[7] Cockburn B, Lin S Y, Shu C W 1989 J. Comput. Phys. 84 90
[8] Cockburn B, Hou S, Shu C W 1990 Math. Comp. 54 545
[9] Cockburn B, Shu C W 1998 J. Comput. Phys. 141 199
[10] Cockburn B, Shu C W 2001 J. Sci. Comput. 16 173
[11] Chen D W, Yu X J 2009 Chin. J. Comput. Phys. 26 501 (in Chinese) [陈大伟, 蔚喜军 2009 计算物理 26 501]
[12] Zhang L, Yuan L 2010 Chin. J. Comput. Phys. 27 509 (in Chinese) [张磊, 袁礼 2010 计算物理 27 509]
[13] Jia Z P, Zhang S D 2011 J. Comput. Phys. 230 2496
[14] Maire P H, Abgrall R, Breil J, Ovadia J 2007 SIAM J. Sci. Comput. 29 1781
[15] Toro E F 1997 Riemann Solvers and Numerical Methods for Fluid Dynamics-a Practical Introduction (2nd Ed.) (Berlin: Springer) p581
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