An unsplit Godunov method for ideal MHD via constrained transport in three dimensions
作者： Thomas A. Gardiner , James M. Stone
DOI: 10.1016/J.JCP.2007.12.017
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摘要: We present a single step, second-order accurate Godunov scheme for ideal MHD which is an extension of the method described in [T.A. Gardiner, J.M. Stone, An unsplit godunov via constrained transport, J. Comput. Phys. 205 (2005) 509] to three dimensions. This algorithm combines corner transport upwind (CTU) Colella multidimensional integration, and (CT) preserving divergence-free constraint on magnetic field. describe calculation PPM interface states 3D must include ''MHD source terms'' naturally respect balance implicit these terms by @?.B=0 condition. compare two different forms CTU integration require either 6- or 12-solutions Riemann problem per cell time-step, detailed description 6-solve algorithm. Finally, we solutions test problems demonstrate accuracy robustness
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Ue‐Li Pen, Phil Arras, ShingKwong Wong, A FREE, FAST, SIMPLE, AND EFFICIENT TOTAL VARIATION DIMINISHING MAGNETOHYDRODYNAMIC CODE Astrophysical Journal Supplement Series. ,vol. 149, pp. 447- 455 ,(2003) , 10.1086/378771
Thomas Gardiner, James McLellan Stone, Nonlinear evolution of the magnetohydrodynamic Rayleigh-Taylor instability Physics of Fluids. ,vol. 19, pp. 094104- 094104 ,(2007) , 10.1063/1.2767666
L. Del Zanna, M. Velli, P. Londrillo, Parametric decay of circularly polarized Alfvén waves: Multidimensional simulations in periodic and open domains Astronomy and Astrophysics. ,vol. 367, pp. 705- 718 ,(2001) , 10.1051/0004-6361:20000455
Steven A. Balbus, John F. Hawley, Instability, turbulence, and enhanced transport in accretion disks Reviews of Modern Physics. ,vol. 70, pp. 1- 53 ,(1998) , 10.1103/REVMODPHYS.70.1
J.U Brackbill, D.C Barnes, The Effect of Nonzero ∇ · B on the numerical solution of the magnetohydrodynamic equations☆ Journal of Computational Physics. ,vol. 35, pp. 426- 430 ,(1980) , 10.1016/0021-9991(80)90079-0
Axel Brandenburg, William H. Matthaeus, Magnetic helicity evolution in a periodic domain with imposed field. Physical Review E. ,vol. 69, pp. 056407- 056407 ,(2004) , 10.1103/PHYSREVE.69.056407
Andrew L. Zachary, Andrea Malagoli, Phillip Colella, A higher-order Godunov method for multidimensional ideal magnetohydrodynamics SIAM Journal on Scientific Computing. ,vol. 15, pp. 263- 284 ,(1994) , 10.1137/0915019
Gábor Tóth, The ∇·B=0 Constraint in Shock-Capturing Magnetohydrodynamics Codes Journal of Computational Physics. ,vol. 161, pp. 605- 652 ,(2000) , 10.1006/JCPH.2000.6519
Thomas A. Gardiner, James M. Stone, An unsplit Godunov method for ideal MHD via constrained transport Journal of Computational Physics. ,vol. 205, pp. 509- 539 ,(2005) , 10.1016/J.JCP.2004.11.016
Jeff Saltzman, An unsplit 3D upwind method for hyperbolic conservation laws Journal of Computational Physics. ,vol. 115, pp. 153- 168 ,(1994) , 10.1006/JCPH.1994.1184