Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
A kinetic beam scheme for relativistic gas dynamics
Journal of Computational Physics
Gas-kinetic schemes for the compressible Euler equations: positivity-preserving analysis
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
On the construction of kinetic schemes
Journal of Computational Physics
Kinetic schemes for the ultra-relativistic Euler equations
Journal of Computational Physics
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
Kinetic flux-vector splitting schemes for the hyperbolic heat conduction
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A Characteristics Based Genuinely Multidimensional Discrete Kinetic Scheme for the Euler Equations
Journal of Scientific Computing
Hi-index | 31.45 |
A second-order accurate kinetic scheme for the numerical solution of the relativistic Euler equations is presented. These equations 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 scheme, is based on the well-known fact that the relativistic Euler equations are the moments of the relativistic Boltzmann equation of the kinetic theory of gases when the distribution function is a relativistic Maxwellian. The kinetic scheme consists of two phases, the convection phase (free-flight) and collision phase. The velocity distribution function at the end of the free-flight is the solution of the collisionless transport equation. The collision phase instantaneously relaxes the distribution to the local Maxwellian distribution. The fluid dynamic variables of density, velocity, and internal energy are obtained as moments of the velocity distribution function at the end of the free-flight phase. The scheme presented here is an explicit method and unconditionally stable. 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. The scheme also satisfies positivity and L1-stability. The scheme can be easily made into a total variation diminishing method for the distribution function through a suitable choice of the interpolation strategy. In the numerical case studies the results obtained from the first-and second-order kinetic schemes are compared with the first-and second-order upwind and central schemes. We also calculate the experimental order of convergence and numerical L1-stability of the scheme for smooth initial data.