Mathematical simulation of viscous gas flows between two coaxially rotating concentric cylinders and spheres

A technique for constructing conservative Godunov-type finite-difference schemes for computing viscous gas flows in cylindrical and spherical coordinates is described. Two- and three-dimensional flows in the gap between two coaxially rotating concentric cylinders and spheres are computed. Various types of vortex flows are simulated, which are also typical for an incompressible fluid. The differences from the incompressible case are noted. The results show that cylindrical and spherical Couette flows can be studied within the framework of the mathematical viscous gas model by applying direct numerical simulation with the use of explicit finite-difference schemes.