An Explicit Discontinuous Galerkin Method for Parallel Compressible Two-Phase Flow Simulations

In this thesis an efficient numerical method is presented to enable simulations with cavitating flow for a pure fluid. The simulation of cavitating flow poses various challenges. On the one hand, the phase transition between the vapor and liquid phase must be considered, and on the other hand a high-resolving numerical method is required, which can resolve the occurring spatial and temporal scales. In addition, in the presence of cavitation, the thermodynamic quantities (e.g. density, pressure) can vary by several orders of magnitude over a very short distance.

The presented method is validated and it is compared to results in literature for one dimensional simulations. The desired convergence rate is reached and the obtained results are in very good agreement with the reference data from the literature. A two dimensional calculation shows water streaming around a hydrofoil producing cavitation. The strong pressure waves arising during the collapse of the cavitation regions are captured by the simulation and resolved in a numerically stable manner. Finally, the framework developed here is applied to a complex, three-dimensional application from the industry to demonstrate the quality of the method and to show that complex multiscale problems can be calculated on several thousand processors in a reasonable time. For this industrial application also the good scaling on a high performance computer is shown.