Simulation of linear and nonlinear advection-diffusion problems by the direct radial basis function collocation method

A simple direct radial basis function collocation method is proposed for the advection-diffusion equations. First, a new scheme of multiquadric radial basis function (RBF) is proposed. Then, the newly-proposed radial basis function can be directly used to deal with the time variable as well as space variables encountered in the advection-diffusion equations. This is realized by considering conventional time steps as collocation points. Numerical results for several advection-diffusion equations with different values of Pe ' clet numbers show that the direct radial basis function collocation method performs well for both linear and nonlinear cases.

Automated summary

The proposed direct radial basis function collocation method is effective for solving advection-diffusion equations with both time and space variables. It performs well for both linear and nonlinear cases, as shown in numerical results with different Peclet numbers.