HIERARCHICALLY PARTITIONED SOLUTION STRATEGY FOR CFD APPLICATIONS .1.THEORY

This two-part paper presents the results of a benchmarked analytical-n umerical investigation into the operational characteristics of a unifi ed parallel processing strategy for implicit fluid mechanics formulati ons. This Hierarchical Poly Tree (HPT) strategy is based on multilevel substructural decomposition. The Tree morphology is chosen to minimiz e memory, communications and computational effort. The methodology is general enough to apply to existing finite difference (FD), finite ele ment (FEM), finite volume (FV) or spectral element (SE) based computer programs without an extensive rewrite of code. In addition to finding large reductions in memory, communications and computational effort a ssociated with a parallel computing environment, substantial reduction s are generated in the sequential mode of application. Such improvemen ts grow with increasing problem size. Along with a theoretical develop ment of general 2-D and 3-D HPT, several techniques for expanding the problem size that the current generation of computers are capable of s olving, are presented and discussed. Among these techniques are severa l interpolative reduction methods. It was found that by combining seve ral of these techniques that a relatively small interpolative reductio n resulted in substantial performance gains. Several other unique feat ures/benefits are discussed in this paper. Along with Part I's theoret ical development, Part II presents a numerical approach to the HPT alo ng with four prototype CFD Applications. These demonstrate the potenti al of the HPT strategy.