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Finite difference formulation for the model of a compressible viscous and heat-conducting micropolar fluid with spherical symmetry

We consider the nonstationary 3D flow of a compressible viscous heat-conducting micropolar fluid in the domain to be a subset of R^3, bounded with two concentric spheres. In the thermodynamical sense the fluid is perfect and polytropic. The homogeneous boundary conditions for velocity, microrotation, heat flux and spherical symmetry of the initial data are proposed. This spherically symmetric problem in Eulerian coordinates is transformed to the 1D problem in Lagrangian coordinates in the domain that is a segment. We define then the finite difference approximate equations system and construct the sequence of approximate solu- tions to our problem. By investigating the properties of these approximate solutions, we establish their convergence to the generalized solution of our problem globally in time. Numerical experiments are performed by solving the proposed finite difference formulation. We compare the numerical results obtained by using the finite difference and the Faedo-Galerkin approach and investigate the convergence to the stationary solution.

micropolar fluid flow; spherical symmetry; finite difference approximations; numerical simulations

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