Open Physics (Mar 2021)

Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena

  • Wang Fuzhang,
  • Zheng Kehong,
  • Ahmad Imtiaz,
  • Ahmad Hijaz

DOI
https://doi.org/10.1515/phys-2021-0011
Journal volume & issue
Vol. 19, no. 1
pp. 69 – 76

Abstract

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In this study, we propose a simple direct meshless scheme based on the Gaussian radial basis function for the one-dimensional linear and nonlinear convection–diffusion problems, which frequently occur in physical phenomena. This is fulfilled by constructing a simple ‘anisotropic’ space–time Gaussian radial basis function. According to the proposed scheme, there is no need to remove time-dependent variables during the whole solution process, which leads it to a really meshless method. The suggested meshless method is implemented to the challenging convection–diffusion problems in a direct way with ease. Numerical results show that the proposed meshless method is simple, accurate, stable, easy-to-program and efficient for both linear and nonlinear convection–diffusion equation with different values of Péclet number. To assess the accuracy absolute error, average absolute error and root-mean-square error are used.

Keywords