Numerical Solution of Two-Dimensional Incompressible Power-Law Fluids Using Pseudo-Compressibility Method

A numerical method using the pseudo-compressibility method is applied to the analysis of the two-dimensional flow of power-law fluids. Based on the method of lines, the rational Runge -Kutta time integration scheme is combined with the central finite difference approximation for spacial discretization. The residual averaging is incorporated into the basic scheme in order to accelerate the convergence rate to a steady-state solution. The pseudo-compressibility parameter is adjusted corresponding to Reynolds number and computational grids so that the stability of computation can be significantly enhanced especially for low-Reynolds-number flow. Two kinds of 2 to 1 contraction flow through two-dimensional passages are analyzed with power indices 0.1 ≤ n ≤ 2.0, and at Reynolds number Re=100 and Re=0.01. The numerical results for velocity and pressure gradient profiles and for shear stress at the wall are in agreement with theoretical ones.