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Numerical Simulations for Viscous Reactive Micropolar Real Gas Flow

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Abstract

Micropolar fluids represent a fluid model that, unlike the classic model, does not only describe behavior at the macro level but also deals with fluid behavior at the microlevel. Describing microphenomena in this case was achieved through the introduction of a new hydrodynamic variable called microrotation. This work describes the micropolar gas model with special emphasis on the reactive micropolar gas, focusing on the initial boundary value problem describing the behavior of the micropolar reactive real gas in tubes with solid and thermally insulated walls. In other words, homogeneous boundary conditions for velocity, microrotation, and heat flux are studied. For the mentioned initial boundary value problem, the construction of the Faedo-Galerkin approximations and the corresponding numerical method for obtaining a numerical solution are described. The given numerical method was additionally analyzed with respect to the complexity of the initial conditions in terms of the number of terms in their Fourier expansions.

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An initial-boundary value problem for one-dimensional flow of a compressible viscous heat-conducting micropolar fluid is considered. It is assumed that the fluid is thermodynamically perfect and polytropic. This problem has a unique strong solution on ]0, 1[×]0, T[, for each T > 0 ([7]). We also have some estimations of the solution independent of T ([8]). Using these results we prove a stabilization of the solution.