A Three-Dimensional Model of a Spherically Symmetric, Compressible Micropolar Fluid Flow with a Real Gas Equation of State

Abstract

In this work, we analyze a spherically symmetric 3D flow of a micropolar, viscous, polytropic, and heat-conducting real gas. In particular, we take as a domain the subset of R3 bounded by two concentric spheres that present solid thermoinsulated walls. Also, here, we consider the generalized equation of state for the pressure in the sense that the pressure depends, as a power function, on the mass density. The model is based on the conservation laws for mass, momentum, momentum moment, and energy, as well as the equation of state for a real gas, and it is derived first in the Eulerian and then in the Lagrangian description. Through the application of the Faedo–Galerkin method, a numerical solution to a corresponding problem is obtained, and numerical simulations are performed to demonstrate the behavior of the solutions under various parameters and initial conditions in order to validate the method. The results of the simulations are discussed in detail.

Keywords

• micropolar real gas
• spherical symmetry
• generalized pressure function
• numerical solution