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Upwind numerical approximations of a compressible 1d micropolar fluid flow

In this paper we consider the numerical approximations of the nonstationary 1D flow of the compressible micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The flow equations are considered in Eulerian formulation. It is proved that the inviscid micropolar flow equations are hyperbolic and the corresponding eigensystem is determined. The numerical approximation is 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. The numerical results for the inviscid flow show that the numerical scheme approximate the solutions very accurately. The numerical test for the viscous and heat conducting flow are also performed.

micropolar fluid flow ; hyperbolic conservation law ; upwind scheme ; finite volume approximations

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