Parallel Simulation of the Shallow Water Equations on Structured Dynamically Adaptive Triangular Grids.
Csaba Vigh · mediaTUM – the media and publications repository of the Technical University Munich (Technical University Munich) · 2012
One of the most important computational challenges in the context of the numerical treatment of Partial Differential Equations is the generation, management, and dynamic adaptivity of grids.Dynamic adaptivity is extremely important in applications that require frequent changes of the grid pattern during a simulation run.One such application example is Tsunami simulation, where waves must be tracked with highly resolved local grids.Arbitrary unstructured grids that can handle dynamic adaptivity have a considerable memory and computing time overhead.Therefore, the focus of this work is on the Sierpinski space-filling curvebased, recursively structured and dynamically adaptive triangular grid management system.Space trees recursively split the geometrical domain into smaller sub-domains according to certain predefined sub-division rules.In this thesis we concentrate on the recursive splitting of triangles.The depth-first traversal of the binary refinement tree inherently orders the leaf triangles according to the Sierpinski space-filling curve.We address the challenges of traversal and management of the dynamically adaptive triangular grid, in serial and parallel computing environment.The target application is the parallel simulation of a simplified version of the shallow water equations.