Better numerical algorithms are needed to effectively utilize the current and next generation parallel supercomputers. The numerical algorithms must not be limited in application but must efficiently solve the most challenging scientific and engineering problems. Proposed is an Improved Element-by-Element (IEBE) algorithm applied to Computational Fluid Dynamics (CFD) problems. The algorithm encompasses the advantages of existing EBE methods and expands the algorithm capability by utilizing direct solution techniques, a generalized geometry formulation, and unrestricted material properties and equation formulation. The research will derive, validate, and demonstrate the algorithm and benchmark the performance. The principal investigator and consultant together provide expertise in CFD and algorithm development. The research could dramatically impact the way in which CFD and other application problems are performed in parallel computer environments by industry and government.
