Modelling and entropy satisfying relaxation scheme for the nonconservative bitemperature Euler system with transverse magnetic field

The present paper concerns the study of nonconservative bitemperature Euler system with transverse magnetic field. We firstly introduce an underlying conservative kinetic model coupled to Maxwell equations. field is then established from this by hydrodynamic limit. Next we derivation a finite volume method approximate weak solutions. It obtained solving relaxation Suliciu type, and similar HLLC type solvers. solver shown in particular preserve positivity density internal energies. Moreover use local minimum entropy principle prove discrete inequalities, ensuring robustness scheme.