Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics
Journal of Computational Physics
An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Wave propagation algorithms for multidimensional hyperbolic systems
Journal of Computational Physics
Multidimensional upwinding. Part I. The method of transport for solving the Euler equations
Journal of Computational Physics
Multidimensional upwinding. Part II. Decomposition of the Euler equations into advection equations
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Evolution Galerkin methods for hyperbolic systems in two space dimensions
Mathematics of Computation
Two-dimensional Riemann solver for Euler equations of gas dynamics
Journal of Computational Physics
Vorticity-Preserving Lax--Wendroff-Type Schemes for the System Wave Equation
SIAM Journal on Scientific Computing
Finite volume evolution Galerkin methods for nonlinear hyperbolic systems
Journal of Computational Physics
Finite Volume Evolution Galerkin Methods for Hyperbolic Systems
SIAM Journal on Scientific Computing
Application of space-time CE/SE method to shallow water magnetohydrodynamic equations
Journal of Computational and Applied Mathematics
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
Journal of Computational Physics
Finite volume evolution Galerkin (FVEG) methods for three-dimensional wave equation system
Applied Numerical Mathematics
Journal of Computational Physics
Applied Numerical Mathematics
Numerical study of shear-dependent non-Newtonian fluids in compliant vessels
Computers & Mathematics with Applications
Journal of Computational Physics
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In this paper we propose a new finite volume evolution Galerkin (FVEG) scheme for the shallow water magnetohydrodynamic (SMHD) equations. We apply the exact integral equations already used in our earlier publications to the SMHD system. Then, we approximate these integral equation in a general way which does not exploit any particular property of the SMHD equations and should thus be applicable to arbitrary systems of hyperbolic conservation laws in two space dimensions. In particular, we investigate more deeply the approximation of the spatial derivatives which appear in the integral equations. The divergence free condition is satisfied discretely, i.e. at each vertex. First numerical results confirm reliability of the numerical scheme.