Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics
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 kinetic beam scheme for relativistic gas dynamics
Journal of Computational Physics
A flux-split algorithm applied to relativistic flows
Journal of Computational Physics
On the Analysis of Finite Volume Methods for Evolutionary Problems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Evolution Galerkin methods for hyperbolic systems in two space dimensions
Mathematics of Computation
Finite volume evolution Galerkin methods for nonlinear hyperbolic systems
Journal of Computational Physics
Kinetic schemes for the relativistic gas dynamics
Numerische Mathematik
Finite Volume Evolution Galerkin Methods for Hyperbolic Systems
SIAM Journal on Scientific Computing
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
Journal of Computational Physics
The finite volume local evolution Galerkin method for solving the hyperbolic conservation laws
Journal of Computational Physics
Riemann Solver for Relativistic Hydrodynamics
Journal of Computational Physics
A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics
Journal of Computational Physics
A direct Eulerian GRP scheme for relativistic hydrodynamics: One-dimensional case
Journal of Computational Physics
A direct Eulerian GRP scheme for relativistic hydrodynamics: Two-dimensional case
Journal of Computational Physics
The space-time CESE method for solving special relativistic hydrodynamic equations
Journal of Computational Physics
Journal of Computational Physics
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The paper proposes a second-order accurate finite volume local evolution Galerkin (FVLEG) method for two-dimensional special relativistic hydrodynamical (RHD) equations. Instead of using the dimensional splitting method or solving one-dimensional local Riemann problem in the direction normal to cell interface, the FVLEG method couples a finite volume formulation with the (genuinely) multi-dimensional approximate local evolution operator, which is derived by evolving the solutions of corresponding locally linearized RHD equations along all bicharacteristic directions. Several numerical examples are given to demonstrate the accuracy and the performance of the proposed FVLEG method.