A compact 9 point stencil based on integrated RBFs for the convection-diffusion equation

作者：Mai Duy N^*; Thai Quang N; Hoang Trieu T T; Tran Cong T

来源：Applied Mathematical Modelling, 2014, 38(4): 1495-1510.

DOI：10.1016/j.apm.2013.08.017

• Compact local stencils
• High-order approximations
• Convection-diffusion equation
• Integrated radial basis functions

In this paper, a high-order compact stencil for solving the convection-diffusion equation in two dimensions is proposed. The convection and diffusion terms are both approximated by means of radial basis functions (RBFs) that are constructed over 3 x 3 rectangular stencils. Salient features here are that (i) integration is employed to construct local RBF approximations; and (ii) through the constants of integration, values of the convection-diffusion equation at several selected nodes on the stencil are also enforced. Numerical results indicate that (i) the inclusion of the governing equation into the stencil leads to a significant improvement in accuracy; (ii) when the convection dominates, accurate solutions are obtained at a regime of the RBF width which makes the RBFs peaked; and (iii) high levels of accuracy are achieved using relatively coarse grids.

• 出版日期2014-2-15