Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics
Journal of Computational Physics
Boltzmann type schemes for gas dynamics and the entropy property
SIAM Journal on Numerical Analysis
Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions
SIAM Journal on Numerical Analysis
Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms
Journal of Computational Physics
Multidimensional upwinding. Part I. The method of transport for solving the Euler equations
Journal of Computational Physics
Multidimensional upwinding. Part II. Decomposition of the Euler equations into advection equations
Journal of Computational Physics
Discrete Kinetic Schemes for Multidimensional Systems of Conservation Laws
SIAM Journal on Numerical Analysis
A wave propagation method for three-dimensional hyperbolic conservation laws
Journal of Computational Physics
Second-order accurate kinetic schemes for the ultra-relativistic Euler equations
Journal of Computational Physics
Finite Volume Evolution Galerkin Methods for Hyperbolic Systems
SIAM Journal on Scientific Computing
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Journal of Scientific Computing
Journal of Computational Physics
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In this paper we present the results of a kinetic relaxation scheme for an arbitrary hyperbolic system of conservation laws in two space dimensions. We propose a new discrete velocity Boltzmann equation, which is an improvement over the previous models in terms of the isotropic coverage of the multidimensional domain by the foot of the characteristic. The discrete kinetic equation is solved by a splitting method consisting of a convection step and a collision step. The convection step involves only the solution of linear transport equations whereas the collision step instantaneously relaxes the distribution function to a local Maxwellian. An anti-diffusive Chapman-Enskog distribution is used to derive a second order accurate method. Finally some numerical results are presented which confirm the robustness and correct multidimensional behaviour of the proposed scheme.