Application of space-time CE/SE method to shallow water magnetohydrodynamic equations

Journal of Computational and Applied Mathematics

Volumn 196, Issue 1, 2006, Pages 132-149

  Qamar, Shamsul ^a   Warnecke, Gerald ^a  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

CE SE method; Conservation laws; Discontinuous solutions; Hyperbolic systems; Shallow water magnetohydrodynamic equations

Indexed keywords

APPROXIMATION THEORY; CONSERVATION; MATHEMATICAL MODELS; PROBLEM SOLVING; WATER; WAVE PROPAGATION;

CONSERVATION LAWS; DISCONTINUOUS SOLUTIONS; HYPERBOLIC SYSTEMS; MAGNETIC EQUILIBRIUM; SHALLOW WATER MAGNETOHYDRODYNAMIC EQUATIONS; SPACE-TIME CE/SE METHOD;

MAGNETOHYDRODYNAMICS;

EID: 33745650298     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.08.014     Document Type: Article

References (20)

1. Brackbill J.U., and Baranes D.C. The effect of nonzero ∇ · B on the numerical solution of the magnetohydrodynamic equations. J. Comput. Phys. 35 (1980) 426-430
2. Chang S.C. The method of space time conservation element and solution element-a new approach for solving the Navier Stokes and Euler equations. J. Comput. Phys. 119 (1995) 234-295
3. S.C. Chang, Courant number insensitive CE/SE schemes, AIAA Paper 2002-3890 (2002).
4. S.C. Chang, X.Y. Wang, Multi-dimensional courant number insensitive CE/SE Euler solvers for applications involving highly nonuniform meshes, AIAA Paper 2003-5285 (2003).
5. S.C. Chang, X.Y. Wang, C.Y. Chow, New developments in the method of space-time conservation element and solution element-applications to two-dimensional time-marching problems, NASA TM 106758, December 1994.
6. Chang S.C., Wang X.Y., and Chow C.Y. The space-time conservation element and solution element method: a new high resolution and genuinely multidimensional paradigm for solving conservation laws. J. Comput. Phys. 156 (1999) 89
7. De Sterck H. Hyperbolic theory of the shallow water magnetohydrodynamics. Phys. Plasmas 8 (2001) 3293-3304
8. Gilman P.A. Magnetohydrodynamic shallow water equations for the solar tachocline. Astrophys. J. Lett. 544 (2000) 79-82
9. T. Kröger, M. Lukáčová-Medvidová, An evolution Galerkin scheme for the shallow water magnetohydrodynamic (SMHD) equations in two space dimensions, J. Comput. Phys. 206 (2005) 122-149.
10. Lukáčová-Medvid'ová M., and Saibertova M. Genuinely multidimensional evolution Galerkin scheme for the shallow water equations. In: Brezzi F., et al. (Ed). Numerical Mathematics and Advanced Applications (2002), World Scientific Publishing Company, Singapore 105-114
11. Orszag S.A., and Tang C.M. Small-scale structure of two-dimensional magnetohydrodynamic turbulence. Fluid Mech. J. 90 (1979) 129
12. J.A. Rossmanith, A wave propagation method with constrained transport for ideal and shallow water magnetohydrodynamics, Ph.D. Thesis, University of Washington, Seattle, Washington, 2002.
13. Spiegel E.A., and Zahn J.-P. The solar tachocline. Astron. Astrophys. 265 (1992) 106-114
14. E.F. Toro, Shock-capturing Methods for Free Surface Shallow Fluids, vol.2, Wiley, New York, 1962.
15. Tóth G. The ∇ · B = 0 constraint in shock-capturing magnetohydrodynamics codes. J. Comput. Phys. 161 (2000) 605-652
16. X.Y. Wang, C.Y. Chow, S.C. Chang, Application of the space-time conservation element and solution element method to two-dimensional advection-diffusion problems, NASA TM 106946, June 1995.
17. Zhang Z.-C., Yu S.T., and Chang S.C. A space-time conservation element and solution element method for solving the two-dimensional unsteady Euler equations using quadrilateral and hexahedral meshes. J. Comput. Phys. 175 (2002) 168-199
18. Z.-C. Zhang, S.T. Yu, S.C. Lin, S.C. Chang, I. Blankson, Solving the MHD equations by the CE/SE method with and without a projection method for Div B = 0, AIAA J. 42(12) (2004) 311-326, 2605-2608.
19. Zhang Z.-C., Yu S.T., and Lin S.C. Solving the MHD equations by the CE/SE method with and without a projection method for Div B = 0. Trans. Aeronautical Astronautical Soc. Republic China 36 (2004) 311-326
20. Z.-C. Zhang, S.T. Yu, S.C. Lin, S.C. Chang, I. Blankson, Application of the space-time conservation element and solution element method to the ideal magnetohydrodynamics equations, AIAA Paper 2002-3888, 2004.