Numerical simulation of generalized Oldroyd-B and generalized Newtonian fluid flows

Abstract

This paper is dealing with numerical simulation of generalized Newtonian and generalized Oldroyd-B fluids with the aim of blood flow simulation. The Newtonian model of a fluid cannot capture all the phenomena in many fluids with complex microstructure, such as polymers, suspensions (also many biological fluids) and granular materials. The motion of polymeric fluids is described by the conservation of mass and momentum. One shall assume that the fluid is incompressible and temperature variations are negligible. When one considers viscoelastic behavior of polymeric fluids, the extra stress tensor depends not only on the current motion of the fluid, but also on the history of the motion. In this case the extra stress tensor is decomposed into its Newtonian part and its elastic part. Components of the elastic part of the extra stress tensor are computed using the Oldroyd-B constitutive equation. Time derivative of the pressure is added into the continuity equation (Artificial compressibility method) and the arising system of equations is discretized in space with Finite volume method and numerically solved in time with Runge-Kutta method. Numerical methods are tested in the geometry of constricted channel.