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Oliver Christian Fortmeier Parallel Re-Initialization of Level Set Functions and Load Balancing for Two-Phase Flow Simulations

157 Seiten, Dissertation Rheinisch-Westfälische Technische Hochschule Aachen (2011), Softcover, A5

Two-phase flow problems constitute a key element in various areas of computational science and engineering. These flows occur in systems that contain two spatially separated regions which vary over time. Simulations of such flow problems typically result in large amount of computational work and memory requirements. To cope with these requirements for meaningful problem sizes, employing high-performance computers is indispensable as they provide both, the necessary compute power and sufficient memory.

Serial algorithms exist to simulate three-dimensional two-phase flows on adaptive refined, unstructured tetrahedral grids by the level set approach. However, for such simulations, there is a lack of parallel algorithms to efficiently employ high-performance computers. The two main new contributions of this thesis address the gap of missing parallel algorithms. First, different load balance models are systematically developed to decompose the computational work of two-phase flow simulations among compute units. These models include a novel hypergraph model. Second, a parallel re-initialization algorithm is presented to retransform level set functions to a signed distance function. This new algorithm relies on direct distance computations and is designed to exploit the architecture of today’s high-performance computers which consist of a cluster of multi-core processors.

This thesis also presents a detailed evaluation to demonstrate the general applicability of these new algorithmic approaches in the context of two-phase flow simulations. To this end, all presented methods are implemented in the software DROPS which is being developed in collaboration with the Chair for Numerical Mathematics at RWTH Aachen University.