Numerical Simulation of a Three-dimensional Bingham Fluid Flow

Dipl.-Ing. Philipp Laaber

April 1, 2008, 3:30 p.m. T 1010

Non-Newtonian fluids, especially Bingham fluids, are widely used in practice. The numerical simulation of such flows involves many mathematical problems. In this talk we present two numerical methods for computing a Bingham fluid flow in a three-dimensional domain. Both methods are based on an existing algorithm for a two-dimensional problem.

Starting from a classical formulation for several problems, we will derive mixed as well as dual dual formulations for two problems. We will proof existence and uniqueness of a solution. The two-dimensional algorithm is extended in two different ways into three dimensions. The discretization of both problems is done by finite elements. At the end numerical results for both realizations confirm the mathematical theory.