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The Numerical Approximations of the Solution for the Piston Problem With Viscous Compressible Micropolar Fluid

We consider the one dimensional flow of a compressible viscous and heat-conducting micropolar fluid, which is in thermodynamical sense perfect and polytropic. In the first part of the work we will derive the model for the piston problem of described fluid with non homogeneous boundary conditions and analyze the existence and uniqueness of the solution, as well as the regularity of the solution. In the last part of the work we will construct the numerical approximations of the solutions based on Faedo-Galerkin method for simple boundary conditions and analyze their convergence.

micropolar fluid; numerical solution; Faedo-Galerkin method; the piston problem

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