Large-scale density-driven flow simulations using parallel unstructured Grid adaptation and local multigrid methods

Advanced parallel applications based on the message-passing paradigm are difficult to design and implement, especially when solution adaptive techniques are used and three-dimensional problems on complex geometries are faced, which yield the use of unstructured Grids. We present the building blocks for a parallel-adaptive scheme for the solution of time-dependent and nonlinear partial differential equations. To minimize computational requirements, h-adaptivity is introduced via parallel, local Grid adaptation. Novel techniques to avoid hanging nodes are introduced, these assure conforming meshes of hybrid element type in three space dimensions. As a core of the adaptive scheme, local multigrid methods are used to solve the arising linear systems rapidly in parallel. Dynamic Grid changes from h-adaptivity lead to load imbalance during run time, therefore dynamic load balancing and migration is performed to exploit the aggregated performance of large processor sets efficiently. Real-world calculations arising from density-driven flow problems in porous media are performed using the presented parallel-adaptive solution strategy. The computations are analyzed with regard to speedup. Timings of Grid adaptation, dynamic load balancing/migration and numerical solution scheme show that large-scale runs on 512 processors gain an overall parallel, numerical speedup of up to 278. A further reduction of the element count by h-adaptivity by a factor of up to 195 shows the enormous capabilities of the presented parallel-adaptive multigrid based solution scheme.