Time dependent boundary conditions for hyperbolic systems
Journal of Computational Physics
A method for incorporating Gauss' lasw into electromagnetic pic codes
Journal of Computational Physics
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
On Godunov-type methods for gas dynamics
SIAM Journal on Numerical Analysis
Notes on the eigensystem of magnetohydrodynamics
SIAM Journal on Applied Mathematics
Journal of Computational Physics
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Hyperbolic divergence cleaning for the MHD equations
Journal of Computational Physics
AN APPROXIMATE RIEMANN SOLVER FOR MAGNETOHYDRODYNAMICS (That Works in More than One Dimension)
AN APPROXIMATE RIEMANN SOLVER FOR MAGNETOHYDRODYNAMICS (That Works in More than One Dimension)
Journal of Computational Physics
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
SIAM Journal on Scientific Computing
Locally Divergence-preserving Upwind Finite Volume Schemes for Magnetohydrodynamic Equations
SIAM Journal on Scientific Computing
A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics
Journal of Computational Physics
Numerical Solutions to Compressible Flows in a Nozzle with Variable Cross-section
SIAM Journal on Numerical Analysis
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
Journal of Computational Physics
Splitting based finite volume schemes for ideal MHD equations
Journal of Computational Physics
Semi-Godunov schemes for multiphase flows in porous media
Applied Numerical Mathematics
A positive MUSCL-Hancock scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Hi-index | 31.45 |
Wave propagation in idealized stellar atmospheres is modeled by the equations of ideal MHD, together with the gravity source term. The waves are modeled as small perturbations of isothermal steady states of the system. We consider a formulation of ideal MHD based on the Godunov-Powell form, with an embedded potential magnetic field appearing as a parameter. The equations are discretized by finite volume schemes based on approximate Riemann solvers of the HLL type and upwind discretizations of the Godunov-Powell source terms. Local hydrostatic reconstructions and suitable discretization of the gravity source term lead to a well-balanced scheme, i.e., a scheme which exactly preserves a discrete version of the relevant steady states. Higher order of accuracy is obtained by employing suitable minmod, ENO and WENO reconstructions, based on the equilibrium variables, to construct a well-balanced scheme. The resulting high order well-balanced schemes are validated on a suite of numerical experiments involving complex magnetic fields. The schemes are observed to be robust and resolve the complex physics well.