Comparison between two common collocation approaches based on radial basis functions for the case of heat transfer equations arising in porous medium

TL;DR

This paper compares two radial basis function collocation methods, IRBF and DRBF, for solving heat transfer equations in porous media, demonstrating IRBF's superior accuracy and convergence in modeling nuclear waste disposal canisters.

Contribution

The study introduces a comparative analysis of IRBF and DRBF methods specifically applied to heat transfer in porous media, highlighting IRBF's enhanced performance.

Findings

IRBF outperforms DRBF in accuracy

IRBF shows faster convergence rates

Numerical results validate IRBF's effectiveness

Abstract

In this paper two common collocation approaches based on radial basis functions have been considered; one be computed through the integration process (IRBF) and one be computed through the differentiation process (DRBF). We investigated the two approaches on natural convection heat transfer equations embedded in porous medium which are of great importance in the design of canisters for nuclear wastes disposal. Numerical results show that the IRBF be performed much better than the common DRBF, and show good accuracy and high rate of convergence of IRBF process.