Load Balancing for Computational Fluid Dynamics Calculations

Many problems in computational fluid dynamics can be solved numerically by representing the flow on a finite set of points, the grid. The solution procedure typically proceeds by repeated application of some calculations for each point x in the grid, using the values of the flow-field in several grid points in a neighbourhood of x. Provided this neighbourhood is not too large, a common way to perform these calculations on a parallel computer, is by employing domain-decomposition. In such a technique, the computational domain is partitioned into subdomains. Each subdomain contains a subset of all the points in the original grid, and is assigned to a processor of the parallel machine. Each processor performs the calculations for the points in the subdomain(s) assigned to it. For the computations for the points on the boundaries between two subdomains, information is needed concerning the flow-field in some points in the neighbouring subdomains. Therefore, the processors have to communicate at regular intervals. E g in the solution of a time-dependent flow-problem, communication will typically take place (at least) every timestep. The parallel computer is used optimally if none of the processors have to wait for information they need from other processors. Therefore it is important to assign subdomains representing appropriate amounts of work to each processor.