Effective Domain Decomposition Meshless Formulation Of Fully-viscous Incompressible Fluid Flows
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E. Divo & A. Kassab
An effective and efficient domain decomposition meshless solution methodology for fully-viscous incompressible fluid flow problems is presented in this paper. The formulation is based on a time-progression decoupling of the equations using a Helmholtz potential. The domain decomposition approach reduces the conditioning numbers of the resulting algebraic systems while increasing efficiency of the solution process and decreasing memory requirements, in addition to rendering the method ideally suited for parallel implementation. Numerical examples are presented to validate the approach by comparing the meshless solutions to Finite Volume Method (FVM) solutions provided by a commercial CFD solver. 1 Introduction Despite their effectiveness in solving fluid problems, classical numerical methods such as finite element methods (FEM) and finite volume methods (FVM) require significant effort for mesh generation. In fact, for most computational fluid dynamics (CFD) models of geometrically complex components encountered routinely in engineering analysis, mesh generation is the most time-consuming and least automated part of the model and analysis.Meshless methods, a class of numerical techniques that rely on global interpolation on non-ordered spatial point distributions, offer the hope of eliminating this major stumbling block.