A high-order finite difference WENO scheme for ideal magnetohydrodynamics on curvilinear meshes
作者： Andrew J. Christlieb , Xiao Feng , Yan Jiang , Qi Tang
DOI:
关键词: Applied mathematics 、 Cartesian coordinate system 、 Finite difference 、 Boundary value problem 、 Riemann solver 、 Solver 、 Mathematics 、 Boundary (topology) 、 Curvilinear coordinates 、 Taylor series
摘要: A high-order finite difference numerical scheme is developed for the ideal magnetohydrodynamic equations based on an alternative flux formulation of weighted essentially non-oscillatory (WENO) scheme. It computes a by Taylor expansion in space, with lowest-order term solved from Riemann solver and higher-order terms constructed physical fluxes limited central differences. The coupled several solvers, including Lax-Friedrichs HLL-type general curvilinear meshes two dimensions verified number benchmark problems. In particular, HLLD Cartesian extended to proper modifications. boundary condition perfect electrical conductor (PEC) derived geometry through bow shock flow. Numerical results also confirm advantages using low dissipative solvers current framework.
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A. Jeffrey, T. Taniuti, Non-Linear Wave Propagation ,(1964)
Tamas I. Gombosi, Kenneth G. Powell, Axisymmetric Modeling of Cometary Mass Loading on an Adaptively Refined Grid: Hydrodynamic Results GMS. ,vol. 84, pp. 237- 246 ,(2013) , 10.1029/GM084P0237
E. F. Toro, M. Spruce, W. Speares, Restoration of the contact surface in the HLL-Riemann solver Shock Waves. ,vol. 4, pp. 25- 34 ,(1994) , 10.1007/BF01414629
Shengtai Li, An HLLC Riemann solver for magneto-hydrodynamics Journal of Computational Physics. ,vol. 203, pp. 344- 357 ,(2005) , 10.1016/J.JCP.2004.08.020
Chi-Wang Shu, Stanley Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes,II Journal of Computational Physics. ,vol. 83, pp. 32- 78 ,(1989) , 10.1016/0021-9991(89)90222-2
Hiroyuki Nishida, Taku Nonomura, Short Note: ADI-SGS scheme on ideal magnetohydrodynamics Journal of Computational Physics. ,vol. 228, pp. 3182- 3188 ,(2009) , 10.1016/J.JCP.2009.01.032
Chi-Wang Shu, High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems Siam Review. ,vol. 51, pp. 82- 126 ,(2009) , 10.1137/070679065
H. De Sterck, A. Csı́k, D.Vanden Abeele, S. Poedts, H. Deconinck, Stationary two-dimensional magnetohydrodynamic flows with shocks: characteristic analysis and grid convergence study Journal of Computational Physics. ,vol. 166, pp. 28- 62 ,(2001) , 10.1006/JCPH.2000.6640
Christiane Helzel, James A. Rossmanith, Bertram Taetz, A High-Order Unstaggered Constrained-Transport Method for the Three-Dimensional Ideal Magnetohydrodynamic Equations Based on the Method of Lines SIAM Journal on Scientific Computing. ,vol. 35, ,(2013) , 10.1137/120870323
K. F. Gurski, An HLLC-Type Approximate Riemann Solver for Ideal Magnetohydrodynamics SIAM Journal on Scientific Computing. ,vol. 25, pp. 2165- 2187 ,(2004) , 10.1137/S1064827502407962