Fluid Structure Interaction using an Arbitrary Lagrangian Eulerian Formulation

Abstract

Multidisciplinary and Multiphysics coupled problems represent nowadays a challenging field when studying even more complex phenomena that appear in nature and in new technologies (e.g. Magneto-Hydrodynamics, Micro-Electro-Mechanics, Thermo-Mechanics, Fluid-Structure Interaction, etc.). Particularly, when dealing with Fluid-Structure Interaction problems several questions arise, namely the coupling algorithm, the mesh moving strategy, the Galilean Invariance of the scheme, the compliance with the Discrete Geometric Conservation Law (DGCL), etc. Therefore, the aim of this thesis is the development and implementation of a coupling algorithm for existing modules or subsystems, in order to carry out FSI simulations with the focus on distributed memory parallel platforms. Regarding the coupling techniques, some results on the convergence of the strong coupling Gauss-Seidel iteration are presented. Also, the precision of different predictor schemes for the structural system and the influence of the partitioned coupling on stability are discussed. Another key point when solving FSI problems is the use of the ‘‘Arbitrary Lagrangian Eulerian formulation’’ (ALE), which allows the use of moving meshes. As the ALE contributions affect the advective terms, some modifications on the stabilizing and the shock-capturing terms, are needed. Also, the movements of the fluid mesh produces a volume change in time of the elements, which adds to the fluid formulation an extra conservation law to be satisfied. The law is known as the Discrete Geometric Conservation Law (DGCL). In this thesis a new and original methodology for developing DGCL compliant formulations based on an Averaged ALE Jacobians Formulation (AJF) is presented. [Dissertation submitted to the Postgraduate Department of FACULTAD DE INGENIERIA Y CIENCIAS HIDRICAS of the UNIVERSIDAD NACIONAL DEL LITORAL in partial fulfillment of the requirements for the degree of Doctor en Ingeniería - Mención Mecánica Computacional. 2011-12-19]