Adaptive Finite Element Methods for Rigid Particulate Flow Problems

Subject of this work is the numerical simulation of the motion of rigid particles in an incompressible viscous or viscoelastic fluid. What makes this task especially challenging is the fact that two different physical models are coupled: The fluid motion is described by a system of partial differential equations (Navier-Stokes equations), while the dynamics of the rigid particles is determined as the solution of a system of ordinary differential equations (Newton's laws of motion). In this work, numerical methods for some prototypical situations are developed, analyzed and validated; all of them are based on the finite element method (FEM). In this context, special emphasis is given to local grid adaptation. The goal is to obtain a high accuracy and, at the same time, to keep the computational effort as low as possible