BGK-based scheme for multicomponent flow calculations
Journal of Computational Physics
A kinetic beam scheme for relativistic gas dynamics
Journal of Computational Physics
A New Perspective on Kinetic Schemes
SIAM Journal on Numerical Analysis
Gas-kinetic Theory Based Flux Splitting Method for Ideal Magnetohydrodynamics
Gas-kinetic Theory Based Flux Splitting Method for Ideal Magnetohydrodynamics
Gas evolution dynamics in Godunov-type schemes and analysis of numerical shock instability
Gas evolution dynamics in Godunov-type schemes and analysis of numerical shock instability
Second-order accurate kinetic schemes for the ultra-relativistic Euler equations
Journal of Computational Physics
Kinetic flux-vector splitting schemes for the hyperbolic heat conduction
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics
Journal of Computational Physics
The space-time CESE method for solving special relativistic hydrodynamic equations
Journal of Computational Physics
Hi-index | 31.47 |
We present a kinetic numerical scheme for the relativistic Euler equations, which describe the flow of a perfect fluid in terms of the particle density n, the spatial part of the four-velocity u and the pressure p. The kinetic approach is very simple in the ultra-relativistic limit, but may also be applied to more general cases. The basic ingredients of the kinetic scheme are the phase-density in equilibrium and the free flight. The phase-density generalizes the nonrelativistic Maxwellian for a gas in local equilibrium. The free flight is given by solutions of a collision free kinetic transport equation. The scheme presented here is an explicit method and unconditionally stable. We establish that the conservation laws of mass, momentum and energy as well as the entropy inequality are everywhere exactly satisfied by the solution of the kinetic scheme. For that reason we obtain weak admissible Euler solutions including arbitrarily complicated shock interactions. In the numerical case studies the results obtained from the kinetic scheme are compared with the first order upwind and centered schemes.