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

Abstract

AbstractAdvanced 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. Copyright © 2005 John Wiley & Sons, Ltd.