An efficient higher order accurate parallel algorithm for aeroacoustic applications

In this paper the problems associated with achieving good performance from a Computational Aeroacoustics (CAA) code on the CM-5 (in an entirely data parallel approach) are addressed. The CAA algorithm requires solving the full 3-D Navier Stokes equations using high order spatial and temporal differencing and nonreflecting boundary conditions, among other things, to preserve the integrity of the acoustic wave solution. The spatial differencing is accomplished with sixth order central differences. A fourth order Runge-Kutta scheme is used for time advancement. Each grid point needs data from eighteen neighboring points to perform the spatia! differencing. Near the boundaries biased stencils are required to maintain high order accuracy. These large, varied stencils present two problems from a parallel processing point of view. One is the large amount of data that has to be communicated and the associated communication time. The other is the large number of stencils required to maintain high accuracy near the boundaries. Specialized treatment of each of the different stencils would provide for a very poorly load balanced (and consequently inefficient) code. The communication time overhead is significantly decreased by organizing the data into blocks and communicating on a block basis instead of an element basis. The specialized boundary treatment problem is all but eliminated by using generalized global stencil arrays so that for a given physical boundary condition all points can be evaluated in parallel. Results indicate a significant performance improvement over a code that doesn’t use the methodologies proposed here. These results are presented in the form of a detailed timing breakdown Per iteration.