Parallelization of a Lagrange-Euler-model for three-dimensional free surface flow and transport processes

Abstract A three-dimensional model for free surface flow and transport processes was parallelized for computer systems with distributed memory . This involved the development of numerical algorithms for an existing serial software system which uses operator - splitting for solving the basic equations. As such it combines Lagrangian and Eulerian concepts through the coupling of Characteristics (explicit) and Finite - Element Methods (implicit). A modular communication interface offering the choice between machine-dependent and portable routines was implemented. The unstructured meshes are partitioned and assigned to the parallel processors applying the Recursive Spectral Bisection method which can be combined with the Kernighan – Lin heuristic . Several problem - independent parallel basic tasks were newly developed. For the iterative solution of simultaneous linear equations, different Conjugate Gradient methods were parallelized for symmetric and non-symmetric matrices using preconditioners specially adapted to the parallel hardware. The Characteristics method is based on an algorithm for tracing path lines which was applied to a parallel system with distributed memory. A field case study of the Weser estuary (North Sea) was chosen to demonstrate the performance of the algorithm on different parallel platforms.