Finite element simulation of the motion of a rigid body in a fluid with free surface

In this work a finite element simulation of the motion of a rigid body in a fluid, with free surface, is described. A completely general referential d escription (of which both Lagrangian and Eulerian descriptions are special cases) of an incompressible, Newtonian fluid is used. Such a description en ables a distorting finite element mesh to be used for the deforming fluid d omain. A new scheme for the linearised approximation of the convective term is pro posed and the improved, second-order accuracy of this scheme is proved. A s econd theorem, which provides a guideline for the artificial adjustment of the Reynolds number when applying a continuation technique, is also proved. The most effective means of eliminating pressure as a variable and enforci ng incompressibility are reviewed. A somewhat novel method to generate fini te element meshes automatically about included rigid bodies, and which invo lves finite element mappings, is described. The approach taken when approximating the free surface, ill that it may Ire treated as a material entity, that is, the material derivative of the free surface is assumed zero. Euler's equations and conservation of linear mome ntum are used to determine the motion of the rigid body. A predictor-correc tor method is used to solve the combined sub-problems. The resulting model is tested in the context of a driven cavity flow, a driven cavity flow with various, included rigid bodies, a die-swell problem, and a stokes second o rder wave. (C) 1999 Elsevier Science S.A. All rights reserved.