Ivan Dražić

Three-dimensional compressible viscous micropolar fluid with cylindrical symmetry: Derivation of the model and a numerical solution

In this paper we consider the nonstationary 3D flow of a compressible viscous and heat-conducting micropolar fluid, which is in the thermodynamical sense perfect and polytropic. The fluid domain is the subset of R3 bounded with two coaxial cylinders that present solid thermoinsulated walls. We assume that the initial mass density, temperature, as well as the velocity and microrotation vectors are radially dependent only. The corresponding solution is also spatially radially dependent. We derive the mathematical model in the Lagrangian description and by using the Faedo–Galerkin method we introduce a system of approximate equations and construct its solutions. We also analyze two numerical examples.

Homogeneous Boundary Problem for the Compressible Viscous and Heat-Conducting Micropolar Fluid Model with Cylindrical Symmetry

We consider nonstationary 3-D flow of a compressible viscous and heat-conducting micropolar fluid which is in the thermodynamical sense perfect and polytropic. We analyze the problem on the domain that is bounded by two coaxial cylinders which present solid thermo-insulated walls. Therefore we assume the cylindrical symmetry of the solution. In this work we present the existence and uniqueness results for corresponding problem with homogeneous boundary data for velocity, microrotation and heat flux, under the additional assumption that the initial density and initial temperature are strictly positive.

Some Properties of a Generalized Solution for 3-D Flow of a Compressible Viscous Micropolar Fluid Model with Spherical Symmetry

We consider the nonstationary 3-D flow of a compressible viscous and heat-conducting micropolar fluid bounded with two concentric spheres that present solid thermoinsulated walls. We assume that the fluid is perfect and polytropic in the thermodynamical sense, as well as that the initial density and temperature are strictly positive. We take sufficiently smooth spherically symmetric initial functions and analyze the corresponding problem with homogeneous boundary data.