engleski

Convergent finite difference scheme for a compressible micropolar fluid flow with a free boundary

In this work the nonstationary flow of the compressible viscous and heat-conducting micropolar fluid is studied. We focus on the fluid flow between a static impermeable solid wall and a free boundary connected to a vacuum state. In the corresponding initial-boundary value problem we suppose that the homogeneous boundary conditions for velocity, microrotation and heat flux on the solid border are valid and that the normal stress, heat flux and microrotation are equal to zero on the free boundary. The aim of this work is to define the convergent numerical scheme for this type of problem and to analyze some numerical solutions. We use the finite difference approach on the staggered mesh and apply it to the model in Lagrangian description to avoid the difficulties associated with the moving boundary in Eulerian coordinate system. It has been shown that the defined scheme is convergent. The numerical solutions obtained by the proposed scheme on the chosen test examples are presented.

micropolar fluid flow; initial-boundary value problem; free boundary; finite difference scheme; strong and weak convergence

nije evidentirano