Comparative study of the multiquadric and thin-plate spline radial basis functions for the transient-convective diffusion problems

DURMUŞ A., Boztosun I., Yasuk F.

INTERNATIONAL JOURNAL OF MODERN PHYSICS C, vol.17, no.8, pp.1151-1169, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 8
  • Publication Date: 2006
  • Doi Number: 10.1142/s0129183106009783
  • Journal Name: INTERNATIONAL JOURNAL OF MODERN PHYSICS C
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1151-1169
  • Keywords: meshless methods, radial basis functions, multiquadric, thin-plate spline, convection-diffusion equations, BOUNDARY-ELEMENT METHODS, HEAT-TRANSFER PROBLEMS, SHAPE-PARAMETERS, PART I, INTERPOLATION, EQUATIONS, IMPLEMENTATION, FORMULATION, COLLOCATION
  • Akdeniz University Affiliated: No

Abstract

The numerical solutions of the unsteady transient-convective diffusion problems are investigated by using multiquadric (MQ) and thin-plate spline (TPS) radial basis functions (RBFs) based on mesh-free collocation methods with global basis functions. The results of radial basis functions are compared with the mesh-dependent boundary element and finite difference methods as well as the analytical solution for high Peclet numbers. It is reported that for low Peclet numbers, MQ-RBF provides excellent agreement, while for high Peclet numbers, TPS-RBF is better than MQ-RBF.