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Claus-Dieter Munz Deputy Director and Head of the Numerical Methods Institute of Aerodynamics and Gas Dynamics, University of Stuttgart
Simulation of compressible two-phase flow with high resolution
Numerical simulations of multi-phase flow in the fully compressible regime is a difficult topic. The difficulties in single phase flow, e.g. the occurrence of multiple scales in turbulent regions, boundary layers and the generation of shock waves, are extended by a phase interface that often strongly influences the flow in a large region around. At the interface, complex thermodynamics is strongly coupled to the hydrodynamics. I will give an overview of the development of numerical methods which resolve two-phase flow by a sharp interface treatment that allows a consistent treatment of the local thermodynamics.
The scheme applies a p-adaptive discontinuous Galerkin scheme in smooth regions. Shocks are captured by a finite volume scheme on a h-refined element-local sub-grid. This sub-cell h-refinement is also used around the phase interface to get a good localization. The resulting hp-adaptive scheme thus combines both, the high order accuracy of the DG method and the robustness of the FV scheme. The sharp interface approximation is established by a level-set ghost fluid method. The local coupling of the bulk phases at the sharp interface considers irreversible local thermodynamics by solving a two-phase Riemann problem.
Both, p-refinement and shock and interface sub-cell resolution are performed at runtime and controlled by an indicator, which based on the modal decay of the solution polynomials. The framework is applied to established benchmarks problems for compressible multiphase flows. The results demonstrate that the hybrid adaptive discretization can efficiently and accurately handle complex multiphase flow problems involving pronounced interface deformations and merging interface contours.