Implementation of a general algorithm for incompressible and compressible flows within the multi-physics code Kratos and preparation of fluid-structure coupling

Abstract

This diploma thesis deals with the implementation of a fluid solver for incompressible and compressible flows within the multi-physics framework Kratos. The presentation of this environment based on the finite element method (FEM) and an introduction to multidisciplinary problems in general are the starting point of this work and help understanding the following steps more easily. Originating from the basic conservation equations for mass, momentum and energy, the Euler equations for inviscid flow are derived. In this context some approximations are presented that avoid the solution of the energy equation and allow the use of a general approach for the simulation of incompressible, slightly compressible and barotropic flow. The implementation of the incompressible case is outlined step-by-step: Having discretized the continuous problem, a fractional step scheme is presented in order to uncouple pressure and velocity components by a split of the momentum equation. Emphasis is placed on the nodal implementation using an edge-based data structure. Moreover, the orthogonal subscale stabilization - necessary because of the finite element discretization - is explained very briefly. Subsequently, the solver is extended to compressible regime mentioning the respective modifications. For validation purposes numerical examples of incompressible and compressible flows in two and three dimensions round of this first part. In a second step, the implemented flow solver is prepared for the fluid-structure coupling. After presenting solving procedures for multi-disciplinary problems, the arbitrary Lagrangian Eulerian (ALE) formulation is introduced and the conservation equations are modified accordingly. Some preliminary tests are performed, particularly with regard to mesh motion and adjustment of the boundary conditions. Finally, expectations for the envisaged fluid-structure coupling are brought forward.