# Numerical Simulation of a Three-dimensional Bingham Fluid Flow

## Dipl.-Ing. Philipp Laaber

**April 1, 2008, 1:30 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.