A kinetic scheme with variable velocities and relative entropy

A new kinetic model is proposed where the equilibrium distribution with bounded support has a range of velocities about two average in 1D. In 2D, function four velocities, one each quadrant. associated finite volume scheme, are used to enforce Rankine-Hugoniot jump conditions for numerical diffusion at cell-interfaces, thereby capturing steady discontinuities exactly. The variable provide additional smooth regions. Further, novel theory based expression relative entropy presented which, along an criterion, identify expansions and flow Appropriate tangency far-field boundary formulated model. Several benchmark 1D 2D compressible test cases solved demonstrate efficacy solver.