A method for incorporating Gauss' lasw into electromagnetic pic codes
Journal of Computational Physics
Simplified second-order Godunov-type methods
SIAM Journal on Scientific and Statistical Computing
An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
On Godunov-type methods near low densities
Journal of Computational Physics
An approximate Riemann solver for ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
On the Choice of Wavespeeds for the HLLC Riemann Solver
SIAM Journal on Scientific Computing
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
A positive conservative method for magnetohydrodynamics based on HLL and Roe methods
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 HLLC Riemann solver for magneto-hydrodynamics
Journal of Computational Physics
HLLC solver for ideal relativistic MHD
Journal of Computational Physics
A simple and accurate Riemann solver for isothermal MHD
Journal of Computational Physics
Splitting based finite volume schemes for ideal MHD equations
Journal of Computational Physics
An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics
Journal of Computational Physics
Piecewise parabolic method on a local stencil for magnetized supersonic turbulence simulation
Journal of Computational Physics
A positive MUSCL-Hancock scheme for ideal magnetohydrodynamics
Journal of Computational Physics
On the role of Riemann solvers in Discontinuous Galerkin methods for magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Adaptive numerical algorithms in space weather modeling
Journal of Computational Physics
E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme
Journal of Computational Physics
Journal of Computational Physics
Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics
Journal of Computational Physics
A HLL-Rankine-Hugoniot Riemann solver for complex non-linear hyperbolic problems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A simple GPU-accelerated two-dimensional MUSCL-Hancock solver for ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.53 |
A new multi-state Harten-Lax-van Leer (HLL) approximate Riemann solver for the ideal magnetohydrodynamic (MHD) equations is developed based on the assumption that the normal velocity is constant over the Riemann fan. This assumption is same as that used in the HLLC (''C'' denotes Contact) approximate Riemann solver for the Euler equations. From the assumption, it is naturally derived that the Riemann fan should consist of four intermediate states for B"x0, whereas the number of the intermediate states is reduced to two when B"x=0. Since the intermediate states satisfied with all jump conditions in this approximate Riemann system are analytically obtained, the multi-state HLL Riemann solver can be constructed straightforwardly. It is shown that this solver can exactly resolve isolated discontinuities formed in the MHD system, and hence named as HLLD Riemann solver. (Here, ''D'' stands for Discontinuities.) It is also analytically proved that the HLLD Riemann solver is positively conservative like the HLLC Riemann solver. Indeed, the HLLD Riemann solver corresponds to the HLLC Riemann solver when the magnetic field vanishes. Numerical tests demonstrate that the HLLD Riemann solver is more robust and efficient than the linearized Riemann solver, and its resolution is equally good. It indicates that the HLLD solver must be useful in practical applications for the ideal MHD equations.