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In this paper, we address a way to reduce the total computational cost ofmeshless approximation by reducing the required stencil size through spatialvariation of computational node regularity. Rather than covering the entiredomain with scattered nodes, only regions with geometric details are coveredwith scattered nodes, while the rest of the domain is discretised with regularnodes. Consequently, in regions covered with regular nodes the approximationusing solely the monomial basis can be performed, effectively reducing therequired stencil size compared to the approximation on scattered nodes where aset of polyharmonic splines is added to ensure convergent behaviour. Theperformance of the proposed hybrid scattered-regular approximation approach, interms of computational efficiency and accuracy of the numerical solution, isstudied on natural convection driven fluid flow problems. We start with thesolution of the de Vahl Davis benchmark case, defined on square domain, andcontinue with two- and three-dimensional irregularly shaped domains. We showthat the spatial variation of the two approximation methods can significantlyreduce the computational complexity, with only a minor impact on the solutionaccuracy.

Spatially-varying meshless approximation method for enhanced computational efficiency