Numerical simulation of Bingham-plastic flow by an upwind finite volume characteristics-based method

A finite volume characteristics-based method has been developed to simulate flow of viscoplastic materials. The artificial compressibility method has been employed to couple the continuity and momentum equations. The method had originally been developed for incompressible Newtonian flows at high Reynolds numbers. In the present paper is shown that accurate solutions can be obtained even for Reynolds numbers less than one. For the case of a Newtonian fluid the present method gives results in excellent agreement with finite element solutions. For the simulation of viscoplastic flow through a slit die and a planar 4:1 contraction the modified Bingham equation proposed by Papanastasiou has been employed. The present results are in very good agreement with numerical solutions published in literature. This work suggests that the proposed method is a promising alternative to finite element methods which are traditionally used in the simulation of non-Newtonian fluids.