The generalized Riemann problem for reactive flows
Journal of Computational Physics
New algorithms for ultra-relativistic numerical hydrodynamics
Journal of Computational Physics
Relativistic hydrodynamics and essentially non-oscillatory shock capturing schemes
Journal of Computational Physics
Extension of the piecewise parabolic method to one-dimensional relativistic hydrodynamics
Journal of Computational Physics
An Iterative Riemann Solver for Relativistic Hydrodynamics
SIAM Journal on Scientific Computing
A two-dimensional conservation laws scheme for compressible flows with moving boundaries
Journal of Computational Physics
A flux-split algorithm applied to relativistic flows
Journal of Computational Physics
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
A note on the conservative schemes for the Euler equations
Journal of Computational Physics
Hyperbolic balance laws: Riemann invariants and the generalized Riemann problem
Numerische Mathematik
An adaptive GRP scheme for compressible fluid flows
Journal of Computational Physics
Riemann Solver for Relativistic Hydrodynamics
Journal of Computational Physics
A direct Eulerian GRP scheme for relativistic hydrodynamics: Two-dimensional case
Journal of Computational Physics
The adaptive GRP scheme for compressible fluid flows over unstructured meshes
Journal of Computational Physics
Journal of Computational Physics
Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics
Journal of Computational Physics
The generalized Riemann problems for compressible fluid flows: Towards high order
Journal of Computational Physics
A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics
Journal of Computational Physics
Hi-index | 31.48 |
The paper proposes a direct Eulerian generalized Riemann problem (GRP) scheme for one-dimensional relativistic hydrodynamics. It is an extension of the Eulerian GRP scheme for compressible non-relativistic hydrodynamics proposed in [M. Ben-Artzi, J.Q. Li, G. Warnecke, A direct Eulerian GRP scheme for compressible fluid flows, J. Comput. Phys. 218 (2006) 19-43]. Two main ingredients, the Riemann invariant and the Rankine-Hugoniot jump condition, are directly used to resolve the local GRP in the Eulerian formulation, and thus the crucial and delicate Lagrangian treatment in the original GRP scheme [3] can be avoided. Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed GRP scheme.