Simulation of layered flow in an infinite cylinder with a time-varying radius

We considered a system of magnetohydrodynamic equations which describes a viscous conducting fluid flow in a time-varying domain. The no-slip condition is satisfied at the boundary of the flow domain. The study of such problems is relevant to controlling the incompressible fluid properties by various means such as a volumetric application of a magnetic field, or the flow domain boundary shift. Within the layered fluid flow model, we obtained a class of exact solutions of the magnetohydrodynamic equations for an infinite cylinder with a time-varying radius. The calculation used the control volume approach with a completely implicit time-dependent scheme. The difference analog of differential equations has the second order of accuracy for its spatial variable and the first order of accuracy for time. The exact solutions we found were used to verify the results of the numerical simulation. They match the accuracy of the difference approximations. The calculation results are stable in a series of tests with a decreasing grid spacing.