AN EFFICIENT LAGRANGIAN METHOD FOR THE COMPUTATION OF THREE-DIMENSIONAL REACTIVE FLOWS ON CONCURRENT COMPUTERS

THE ULTIMATE GOAL OF THE PHASE I AND PHASE II EFFORTS OF THIS PROJECT IS TO DEVELOP A FAST O(NLOGN) OR O(N) COMPUTATIONAL METHOD FOR THE TREATMENT OF A THREE-DIMENSIONAL, UNSTEADY, REACTIVE FLOW ON A CONCURRENT COMPUTER. IN THE PHASE I FEASIBILITY STUDY, A ROBUST O(N(4/3)) THREE-DIMENSIONAL VORTEX PARTICLE METHOD IS BEING DEVELOPED. THIS METHOD, BASED ON THE PROPER TREATMENT OF THE NEAR- AND FAR-FIELD VORTEX INTERACTIONS, IS AN IMPROVEMENT OVER THE CLASSICAL O(N(2)) APPROACH. IT USES BOTH LOCAL ANALYTICAL CORRECTIONS AND FAR-FIELD APPROXIMATIONS. THE METHOD IS BEING IMPLEMENTED ON A MULTIPROCESSOR COMPUTER, USING TWO SETS OF COMMUNICATION STRUCTURE. THIS STRUCTURE ALLOWS THE LOCAL AND GLOBAL INTERPROCESSOR COMMUNICATIONS, USED FOR THE NEAR- AND FAR-FIELD VORTEX INTERACTIONS, RESPECTIVELY, TO BE TREATED SEPARATELY. IN THE GLOBAL COMMUNICATION PROCESS, THE USE OFTHE FAR-FIELD APPROXIMATIONS IN THE COMPUTATION ALLOWS SIGNIFICANT IMPROVEMENT IN COMMUNICATION TIME. THE COMPLETED COMPUTER CODE WILL BE TESTED ON CLASSICAL PROBLEMSIN PHASE I, AND THE ROBUSTNESS OF THE METHOD AND THE PERFORMANCE OF THE PARALLEL ALGORITHM WILL BE INVESTIGATED. IN THE PHASE II EFFORT, FURTHER IMPROVEMENTS WILL INCLUDE THE COUPLING OF (1) A HIERARCHICAL DATA STRUCTURE TO IMPROVETHE ORDER OF THE METHOD TO O(NLOGN) OR O(N) AND (2) A CONSERVATION EQUATION TO INCLUDE THE EFFECTS OF CHEMICAL REACTIONS. THE INCORPORATION OF FISCOUS EFFECTS THROUGH A CIRCULATION EXCHANGE SCHEME MAY BE ALSO CONSIDERED.