On the Numerical Simulation of Viscoplastic Fluid Flow

Publisher Summary This chapter provides an overview of the main mathematical and computational aspects of viscoplasticity. It discusses Bingham flow in cylinders and cavities; the numerical simulation of nonisothermal, compressible, and thixotropic viscoplastic flow, which is an augmented Lagrangian finite-volume approach; the application of fictitious domain; and methods for the numerical simulation of viscoplastic flow. Among the various classes of non-Newtonian materials, those exhibiting viscoplastic properties are particularly interesting in accordance with their ability to strain only if the stress intensity exceeds a minimum value. Many industrial processes involve viscoplastic fluids. The chapter mentions only a few of them—namely, mud, cement slurries, food, waxy crude oils, suspensions, emulsions, foams, etc. In a viscoplastic fluid flow, the flow pattern highlights two kinds of regions: the regions where the stress intensity exceeds the yield stress and the regions where it does not. The former and latter regions are usually called the “yielded” and “unyielded” regions, respectively. The most commonly encountered viscoplastic model is the Bingham fluid.