The introduction of the computer into engineering techniques has resulted in the growth of a completely new field termed computational fluid dynamics (CFD). This field has led to the development of new mathematical methods for solving the equations of fluid mechanics. These improved methods have permitted advanced simulations of flow phenomena on the computer for a wide variety of applications. This leads to a demand for computers which can manage these extremely time consuming calculations within acceptable runtimes. Many of the numerical methods used in computational fluid dynamics are inherently parallel, so that the appearance of parallel computers makes them a promising candidate for this task.
One problem arising when implementing parallel algorithms is the lack of standards both on the hardware and software side. As things like processor topology, parallel operating system, programming languages, etc. have a much greater influence on parallel than on sequential algorithms, one has to choose an environment where it is possible to get results which can be generalized to a larger set of other environments. We think that future supercomputers will be massively parallel systems of the MIMD class with distributed memory and strong communication capabilities. On the software side it seems that some standards could be established in the near future. As our algorithm is designed for message passing environments, this standard might be MPI (Message Passing Interface) [6].
In the CFD field there is another important point: the numerical methods for the solution of the given equations. As we are mainly computer scientists, we decided not to invent new mathematical concepts but to develop an efficient parallel version of an algorithm which was developed by experienced engineers for sequential computers and which is suitable for the solution of problems in the field of turbomachinery [1]. The hardware platforms which are availiable for us, are Transputer systems of different sizes, which fulfill the demands mentioned above. At the time the algorithm was developed, there was no MPI-environment availiable for our transputer systems, so here we will present a version using Parix (Parallel extensions to Unix, a parallel runtime system for Parsytec machines) that needs only a small number of parallel routines, which are common in most message passing environments. Most of these routines are hidden inside a few communication procedures, so that they can be replaced easily, when changing the parallel environment.
The following two sections give a brief overview about the physical and mathematical foundations of the used numerical methods (for a detailed description see [1,2]) and an outline of the general parallelization strategy, including a comparison with other approaches (see also [3,4]). The next section describes in detail some grid division algorithms which are a very important part for this kind of parallel algorithms, because they determine the load balancing between processors. The special subjects of adaptive refinements and dynamic load balancing are discussed in a separate section. Then some results will be presented, while the last section closes with a conclusion and suggestions for further research.