  In this paper, we address a way to reduce the total computational cost of
meshless approximation by reducing the required stencil size through spatial
variation of computational node regularity. Rather than covering the entire
domain with scattered nodes, only regions with geometric details are covered
with scattered nodes, while the rest of the domain is discretised with regular
nodes. Consequently, in regions covered with regular nodes the approximation
using solely the monomial basis can be performed, effectively reducing the
required stencil size compared to the approximation on scattered nodes where a
set of polyharmonic splines is added to ensure convergent behaviour. The
performance of the proposed hybrid scattered-regular approximation approach, in
terms of computational efficiency and accuracy of the numerical solution, is
studied on natural convection driven fluid flow problems. We start with the
solution of the de Vahl Davis benchmark case, defined on square domain, and
continue with two- and three-dimensional irregularly shaped domains. We show
that the spatial variation of the two approximation methods can significantly
reduce the computational complexity, with only a minor impact on the solution
accuracy.
