Modelling Steady Convection-Dominated Phenomena by Node-Adaptive Radial Point Interpolation Meshfree Method (RPIM) with Various RBFs

Abstract

Abstract For numerically solving PDEs, node or grid adaptation schemes have been invented, applied, and improved mainly to improve solution accuracy while reducing the burden caused by CPU-limitation and/or users’ interference. This becomes crucial particularly for problems involving strong changes in physical phenomena. This work proposes a means of node-adaptation used in conjunction with a numerical meshfree method called ‘radial point interpolation (RPIM)’, carried out using the concept of interpolation via. radial basis functions and hence no grid or mesh required. The proposed method is developed to tackle one of the most challenging problems with convective force being overwhelming in the system. This phenomena is known not to be easily numerically simulated. The proposed node-adaptive scheme is carried out where locally-estimated Péclet number (Pe) being used to indicate the areas of interest, places where nodes are expected to be added or removed. The whole adaptation algorithm is dynamic requiring on user’s interference. When compared to solutions obtained from fixed-node cases and other benchmark work, the results obtained in this work strongly suggest benefits in terms of both solution accuracy improvement and CPU-storage reduction.