On Godunov-type methods for gas dynamics
SIAM Journal on Numerical Analysis
An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
An Accurate and Robust Flux Splitting Scheme for Shock and Contact Discontinuities
SIAM Journal on Scientific Computing
Approximate Riemann solvers, parameter vectors, and difference schemes
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Journal of Computational Physics
Journal of Computational Physics
Mass flux schemes and connection to shock instability
Journal of Computational Physics
Divergence-free adaptive mesh refinement for Magnetohydrodynamics
Journal of Computational Physics
Cures for the shock instability: development of a shock-stable Roe scheme
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
We have developed a numerical simulation scheme for three-dimensional magnetohydrodynamical flow with shocks. The numerical scheme is based on the Roe-type scheme and includes additional numerical diffusion in the direction tangential to the shock front to care the carbuncle instability. The numerical viscosity is added only in the regions where the characteristics of either fast or slow wave converges, i.e., in the regions potentially dangerous to the carbuncle instability. Accordingly the numerical viscosity is as small as that of the Roe scheme except near the shock fronts. It is demonstrated from comparison with the HLLE scheme that the magnetic Reynolds number is higher in the simulations obtained with our scheme. We show application of the scheme to the magnetohydrodynamical simulations of type II supernova. It is also proved that the scheme is free from the odd-even decoupling.