Date of Award

Spring 1-1-2011

Document Type


Degree Name

Master of Science (MS)

First Advisor

Mettupalayam V. Sivaselvan

Second Advisor

Harihar Rajaram

Third Advisor

Richard A. Regueiro


The goal of this thesis is to build a clear understanding of the Arbitrary Lagrangian Eulerian (ALE) method and to develop a useful simple implementation. A review of the ALE method is presented with precise notations and detailed explanation of the combined kinematics. As an application, a complete model of fluid-rigid body interaction is developed. Starting from the Navier-Stokes equations, ALE governing equations for the fluid are derived. They are discretized in space using the Finite Element method. Coupled with the rigid body equation of motion via compatibility and equilibrium interface conditions, they lead to a nonlinear system of equations. The latter is solved using an approximated Newton's method. Details on the implementation are given to illustrate the numerical solution procedure. In particular, the prescription of the mesh motion, specific to the ALE method, is developed. The simple pure fluid problem of the Couette flow is used to test the implementation. The formulation is then used to simulate the free oscillations of a rigid circular cylinder embedded in a viscous fluid.