Upwind numerical approximations of a compressible 1d micropolar fluid flow

In this paper we consider the numerical approximations of the nonstationary 1D flow of a compressible micropolar fluid, which is in the thermodynamical sense perfect and polytropic. The flow equations are considered in the Eulerian formulation. It is proved that the inviscid micropolar flow equations are hyperbolic and the corresponding eigensystem is determined. The numerical approximations are based on the upwind Roe solver applied to the inviscid part of the flux, while the viscous part of the flux is approximated by using central differences. Numerical results for the inviscid flow show that the numerical schemes approximate the solutions very accurately. The numerical tests for the viscous and heat-conducting flow are also performed.