Steady and Unsteady Numerical Solution of Generalized Newtonian Fluids Flow by Runge-Kutta method

Abstract

In this paper the laminar viscous incompressible flow for generalized Newtonian (Newtonian and non‐Newtonian) fluids is considered. The governing system of equations is the system of Navier‐Stokes equations and the continuity equation. The steady and unsteady numerical solution for this system is computed by finite volume method combined with an artificial compressibility method. For time discretization the explicit multistage Runge‐Kutta numerical scheme is considered. Steady state solution is achieved for t→∞ using steady boundary conditions and followed by steady residual behavior. The dual time‐stepping method is considered for unsteady computation. The high artificial compressibility coefficient is used in the artificial compressibility method applied in the dual time τ. The steady and unsteady numerical results of Newtonian and non‐Newtonian (shear thickening and shear thinning) fluids flow in the branching channel are presented.