Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
New algorithms for ultra-relativistic numerical hydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Extension of the piecewise parabolic method to one-dimensional relativistic hydrodynamics
Journal of Computational Physics
Capturing shock reflections: an improved flux formula
Journal of Computational Physics
A kinetic beam scheme for relativistic gas dynamics
Journal of Computational Physics
Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Journal of Computational Physics
Kinetic schemes for the ultra-relativistic Euler equations
Journal of Computational Physics
Kinetic schemes for the relativistic gas dynamics
Numerische Mathematik
A BGK-Type Flux-Vector Splitting Scheme for the Ultrarelativistic Euler Equations
SIAM Journal on Scientific Computing
Application of space-time CE/SE method to shallow water magnetohydrodynamic equations
Journal of Computational and Applied Mathematics
On the application of a variant CE/SE method for solving two-dimensional ideal MHD equations
Applied Numerical Mathematics
Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics
Journal of Computational Physics
Hi-index | 31.45 |
The special relativistic hydrodynamic equations are more complicated than the classical ones due to the nonlinear and implicit relations that exist between conservative and primitive variables. In this article, a space-time conservation element and solution element (CESE) method is proposed for solving these equations in one and two space dimensions. The CESE method has capability to capture sharp propagating wavefront of the relativistic fluids without excessive numerical diffusion or spurious oscillations. In contrast to the existing upwind finite volume schemes, the Riemann solver and reconstruction procedure are not the building blocks of the suggested method. The method differs from previous techniques because of global and local flux conservation in a space-time domain without resorting to interpolation or extrapolation. The scheme is efficient, robust, and gives results comparable to those obtained with more sophisticated algorithms, even in highly relativistic two-dimensional test problems.