Calculation of a flow of viscous fluid on adaptive grids (Q1803484)

Two-dimensional incompressible flow in the region bounded by the walls of a channel with quadratic cross-section and the walls of a cylinder rotating inside this channel is considered. The Navier-Stokes equations written in the vorticity-stream function form are descretized using uniform grid obtained via coordinate transformation. To achieve adaptation of the grid in physical domain, a hyperbolic system is introduced with the vorticity as a control function. The solutions of this system give transformed coordinates as functions of those in physical plane. The algorithm consists of alternative solutions of the discretized Navier-Stokes equations using SOR method and the constructed hyperbolic system using grid characteristic method.