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A numerical solution of a Navier-Stokes problem based on the Weighted Least Squares (WLS) approximation of velocity and pressure fields is presented in this paper. The approximation function is constructed over the local support, i.e., a sub cluster of computational nodes. Besides local approximation of the fields also the pressure-velocity algorithm is constructed locally. The presented solution procedure is demonstrated on two classical fluid-flow benchmark tests, i.e., lid-driven cavity and backward-facing step problem. The method is validated through comparison against already published data on regular nodal distributions and convergence analyses. In addition the method is also tested on irregular nodal distributions. Results are presented in terms of cross-section velocity profiles and convergence plots. [ABSTRACT FROM AUTHOR]

This paper analyses the application of OpenMP parallelization on shared-memory systems, such as the increasingly available multicore systems. The parallelization of the local meshless numerical method is considered. The presented solution procedure is suitable for solving systems of coupled partial differential equations. The superlinear speedup is demonstrated on a solution of the fluid mechanics problem. Local core caches are identified as the source of superlinearity and a set of experiments is performed for the analysis of a cache induced superlinear speedup. For the experiments, a simple algorithm simulating the workload of the local meshless numerical method is used for the method complexity assessment. [ABSTRACT FROM PUBLISHER]