Spatially-varying meshless approximation method for enhanced computational efficiency

TL;DR

This paper introduces a hybrid meshless approximation method that combines scattered and regular nodes, significantly reducing computational costs in fluid flow simulations while maintaining high accuracy.

Contribution

It proposes a novel spatially-varying meshless approximation technique that adapts node distribution to improve efficiency in complex domain simulations.

Findings

Significant reduction in computational complexity.

Minor impact on solution accuracy.

Effective in 2D and 3D irregular domains.

Abstract

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.