Adaptive Time-Dependent CFD on Distributed Unstructured Meshes

Two recent trends in software for CFD problems are the use of unstructured adaptive meshes and the need to implement the software on distributed memory parallel computers. The subject of this paper is the implementation of one particular code of this type for the solution of time-dependent compressible Euler and Navier Stokes problems. The software described here uses the method of lines with the spatial discretisation performed using a cell-centred finite volume scheme on unstructured triangular meshes, [2], to generate an ODE system which is integrated forward in time. Time-integration may be performed using a variety of methods; in the experiments reported here a Theta method algorithm with functional iteration is employed. The code attempts to control both the spatial and temporal errors and to balance them so that the spatial error dominates, [2]. This spatial error control means that the position and density of the mesh points may vary dramatically over the course of an integration. In order to ensure that the mesh is load-balanced as it evolves it is desirable to use a dynamic load-balancing technique. This approach is in contrast to work on regular grids which lend themselves to parallelisation via compiler directives & Fortran 90/HPF and also differs from recent work on a distributed memory compiler for irregular problems, [3], which uses a static mesh decomposition executed at runtime.