Numerical Solution of Incompressible Flow of Power-Law Fluid Using Boundary-Fitted Curvilinear Coordinates.

A numerical method using boundary-fitted curvilinear coordinates (BFC) is applied to compute non-Newtonian flow equations in primitive variable formulations for an incompressible inelastic power-law fluid. The flow equations are solved on a special staggered grid by the method of lines using the rational Runge-Kutta time integration scheme and the central finite difference method for spatial discretization, while the Poisson equation is solved by means of the successive overrelaxation (SOR) method using the modified simplified marker and cell (MSMAC) method. It is concluded that the results using BFC are comparable to those using Cartesian coordinates, and the proposed method can be applied to the numerical solution of flow problems of a power-law fluid in arbitrary computational domains.