Numerical Simulation of Viscous Flow of a Non-newtonian Fluid past an Irregular Solid Obstacle by the Mirror Fluid Method

The mirror fluid method is proposed for simulating viscous tubular flow of a Newtonian or non-Newtonian fluid past an irregular solid obstacle using a simple finite difference method for discretization. Suitable flow parameters in the solid domain are assigned by a mirror relation to ensure the surface segment is subjected to zero net shear and normal forces and the boundary conditions are enforced implicitly on the solid-fluid surface. The SIMPLE scheme and the control volume formulation are used for solving the governing equations and a 5th order weighted ENO scheme is adapted for discretization of the constitutive equations. Some typical numerical examples including Newtonian, power-law, Carreau-Bird and Oldroyd-B fluids past half-circular, triangular or trapeziform obstacles in a straight tube are simulated successfully in a two-dimensional axisymmetric coordinate system.