Parallel re-initialization of level set functions and load balancing for two-phase flow simulations

This thesis addresses parallel algorithms for three-dimensional two-phase flow simulations on adaptively refined unstructured tetrahedra grids. These algorithms are designed to simulate the fluid dynamics of two immiscible phases on recent high-performance computer architectures which, in general, consist of clusters of a large number of multi-core processors. The underlying mathematical model of these two-phase flows is based on the Navier-Stokes equations to describe the fluid dynamics. The level set approach is employed to characterize the two phases. The spatial discretization of these partial differential equations is given by the finite element method whereas the time discretization is performed by an implicit theta scheme. This approach facilitates the description of two-phase flow problems as a sequence of large and sparse systems of linear equations which are efficiently solved by Krylov subspace methods. The computational work of two-phase flow simulations is decomposed among compute cores with distributed memory. To this end, a domain decomposition approach is pursued where the tetrahedra of the underlying hierarchy of triangulations are accordingly distributed. In this thesis, graph and hypergraph partitioning models are introduced which determine tetrahedral decompositions. These models are specifically designed for two-phase flow simulations. A major algorithmic element in such simulations is constituted by the re-initialization algorithm that periodically rebuilds a numerically crucial property of the level set function, namely the signed distance property. This task is addressed by a novel parallel algorithm which is capable of re-initializing level set functions on distributed unstructured triangulations. The numerical results of the presented parallel concepts are gathered by the software toolkit DROPS which is being developed in a collaboration with the Chair of Numerical Mathematics at RWTH Aachen University. The parallel scalability of the methods is demonstrated by detailed numerical experiments on up to 1024 compute cores. Furthermore, all parallel concepts are combined in an engineering relevant case study that is concerned with the analysis of an n-butanol drop in an aqueous phase on a triangulation with a high resolution. This study originates from the collaborative research center SFB 540 at RWTH. Its simulation is too large-in terms of memory and compute time-for sequential computing. Thus, only the parallel techniques presented in this thesis allow to perform this detailed analysis