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.