Vectorial Kinetic Relaxation Model with Central Velocity. Application to Implicit Relaxations Schemes

We apply flux vector splitting (FVS) strategy to the implicit kinetic schemes for hyperbolic systems. It enables to increase the accuracy of the method compared to classical kinetic schemes while still using large time steps compared to the characteristic speeds of the problem. The method also allows to tackle multi-scale problems, such asthelow Machnumber limit, for which wavespeeds with larger atioare involved. We present several possible kinetic relaxation schemes based on FVS and compare them on one-dimensional test-cases. We discuss stability issues for this kind of method