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Convergent finite difference scheme for 1D flow of compressible micropolar fluids

In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. The homogeneous boundary conditions for velocity, microrotation and heat flux are introduced. In order to construct the sequence of approximate solution for our problem, we define the finite difference approximate equations system. We investigate the properties of these approximate solutions and establish their convergence to the strong solution of our problem globally in time. A numerical experiment is performed by solving the defined approximate ordinary differential equations system using strong-stability preserving (SSP) Runge-Kutta schemes for time discretization.

micropolar fluid flow; initial-boundary value problem; finite difference approximations; strong and weak convergence; SSP Runge-Kutta schemes

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