4.7 Article

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

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PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.icheatmasstransfer.2021.105775

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Advection-diffusion equation; Multiquadric; Collocation method; Meshless; Nonlinear problems

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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.
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.

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