A Parallel Meshless Numerical Approach for the Solution of Transport Phenomena

The application of the local meshless numerical method (LRBFCM) for solving a system of coupled partial differential equations (PDE) is explored. The numerical approach is tested on the natural convection based fluid flow problems. The fluid flow part of the solution procedure is coupled locally despite its global nature. Such an approach makes the computations convenient for an implementation on parallel computers. In this paper, the OpenMP based parallelization of the proposed numerical approach is demonstrated. On two cores, a superlinear speedup of 2.5 is confirmed by the performance analysis. The parallelization performance is explored for the classical de Vahl Davis natural convection case. The usability of the meshless numerical framework is demonstrated on highly non-linear and coupled case of solidification of binary alloy, where energy and solute transport govern double natural convection in a domain filled with porous media and free fluid with moving interphases.

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