Nermina Mujaković

Nonhomogeneous Boundary Value Problem for One-Dimensional Compressible Viscous Micropolar Fluid Model: Regularity of the Solution

An initial-boundary value problem for 1D flow of a compressible viscous heat-conducting micropolar fluid is considered; the fluid is thermodynamically perfect and polytropic. Assuming that the initial data are Hölder continuous on and transforming the original problem into homogeneous one, we prove that the state function is Hölder continuous on , for each . The proof is based on a global-in-time existence theorem obtained in the previous research paper and on a theory of parabolic equations.

One-Dimensional Compressible Viscous Micropolar Fluid Model: Stabilization of the Solution for the Cauchy Problem

We consider the Cauchy problem for nonstationary 1D flow of a compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. This problem has a unique generalized solution on for each . Supposing that the initial functions are small perturbations of the constants we derive a priori estimates for the solution independent of , which we use in proving of the stabilization of the solution.

One-Dimensional Flow of a Compressible Viscous Micropolar Fluid: Stabilization of the Solution

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.

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.

GLOBAL SOLUTION TO 1D MODEL OF A COMPRESSIBLE VISCOUS MICROPOLAR HEAT-CONDUCTING FLUID WITH A FREE BOUNDARY

Abstract In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a static solid wall and a free boundary connected to a vacuum state. We take the homogeneous boundary conditions for velocity, microrotation and heat flux on the solid border and that the normal stress, heat flux and microrotation are equal to zero on the free boundary. The proof of the global existence of the solution is based on a limit procedure. We define the finite difference approximate equations system and construct the sequence of approximate solutions that converges to the solution of our problem globally in time.

Numerical analysis of the solutions for 1d compressible viscous micropolar fluid flow with different boundary conditions

The intention of this work is to concern the numerical solutions to the model of the nonstationary 1d micropolar compressible viscous and heat conducting fluid flow that is in the thermodynamical sense perfect and polytropic. The mathematical model consists of four partial differential equations, transformed from the Eulerian to the Lagrangian description, and which are associated with different boundary conditions. By using the finite difference scheme and the Faedo-Galerkin method we make different numerical simulations to the results of our problems. The properties of both numerical schemes are analyzed and numerical results are compared on the chosen test examples. The comparison of the numerical results on problems that have the homogeneous or the non-homogeneous boundary conditions for velocity and microrotation show good agreement of both approaches. However, the advantage of the used finite difference method over the Faedo-Galerkin method lies in the simple implementation of the non-homogeneous boundary conditions and in the possibility of approximation of the free boundary problem on which the Faedo-Galerkin method is not applicable.

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.

Finite Difference Formulation for the Model of a Compressible Viscous and Heat-Conducting Micropolar Fluid with Spherical Symmetry

We are dealing with the nonstationary 3D flow of a compressible viscous heat-conducting micropolar fluid, which is in the thermodynamical sense perfect and polytropic. It is assumed that the domain is a subset of R3 and that the fluid is bounded with two concentric spheres. The homogeneous boundary conditions for velocity, microrotation, heat flux, and spherical symmetry of the initial data are proposed. By using the assumption of the spherical symmetry, the problem reduces to the one-dimensional problem. The finite difference formulation of the considered problem is obtained by defining the finite difference approximate equation system. The corresponding approximate solutions converge to the generalized solution of our problem globally in time, which means that the defined numerical scheme is convergent. Numerical experiments are performed by applying the proposed finite difference formulation. We compare the numerical results obtained by using the finite difference and the Faedo–Galerkin approach and analyze the properties of the numerical solutions.