The Java programming language has a number of features that make it attractive for writing high-quality, portable parallel programs. A pure object formulation, strong typing and the exception model make programs easier to create, debug, and maintain. The elegant threading provides a simple route to parallelism on sharedmemory machines. Anticipating great improvements in numerical performance, this paper presents a suite of simple programs that indicate how a pure Java Navier-Stokes solver might perform. The suite includes a parallel Euler solver. We present results from a 32-processor Hewlett-Packard machine and a 4-processor Sun server. While speedup is excellent on both machines, indicating a high-quality thread scheduler, the single-processor performance needs much improvement.
In this article we discuss a strategy for speeding up the solution of the Navier-Stokes equations on highly complex solution domains such as complete aircraft, spacecraft, or turbomachinery equipment. We have used a nite-volume code for the non-turbulent Navier-Stokes equations as a testbed for implementation of linked numerical and parallel processing techniques. Speedup is achieved by the Tangled Web of advanced grid topology generation, adaptive coupling, and sophisticated parallel computing techniques. An optimized grid topology is used to generate an optimized grid: on the block level such a grid is unstructured whereas within a block a structured mesh is constructed, thus retaining the geometrical exibility of the nite element method while maintaining the numerical e ciency of the nite di erence technique. To achieve a steady state solution, we use grid-sequencing: proceeding from coarse to ner grids, where the scheme is explicit in time. Adaptive coupling is derived from the observation that numerical schemes have di ering e ciency during the solution process. Coupling strength between grid points is increased by using an implicit scheme at the sub-block level, then at the block level, ultimately fully implicit across the whole computational domain. Other techniques include switching numerical schemes and the physics model during the solution, and dynamic deactivation of blocks. Because the computational work per block i s v ery variable with adaptive coupling, especially for very complex ows, we h a ve implemented parallel dynamic load-balancing to dynamically transfer blocks between processors. Several 2D and 3D examples illustrate the functioning of the Tangled Web approach on di erent parallel architectures.
SUMMARYIn this paper the generation of general curvilinear co-ordinate systems for use in selected two-dimensional fluid flow problems is presented. The curvilinear co-ordinate systems are obtained from the numerical solution of a system of Poisson equations. The computational grids obtained by this technique allow for curved grid lines such that the boundary of the solution domain coincides with a grid line. Hence, these meshes are called boundary fitted grids (BFG). The physical solution area is mapped onto a set of connected rectangles in the transformed (computational) plane which form a composite mesh. All numerical calculations are performed in the transformed plane. Since the computational domain is a rectangle and a uniform grid with mesh spacings A( = Aq = 1 (in two-dimensions) is used, the computer programming is substantially facilitated. By means of control functions, which form the r.h.s. of the Poisson equations, the clustering of grid lines or grid points is governed. This allows a very fine resolution at certain specified locations and includes adaptive grid generation. The first two sections outline the general features of BFGs, and in section 3 the general transformation rules along with the necessary concepts of differential geometry are given. In section 4 the transformed grid generation equations are derived and control functions are specified. Expressions for grid adaptation are also presented. Section 5 briefly discusses the numerical solution of the transformed grid generation equations using sucessive overrelaxation and shows a sample calculation where the FAS (full approximation scheme) multigrid technique was employed. In the companion paper (Part II), the application of the BFG method to selected fluid flow problems is addressed.
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