High-Order Finite Difference Schemes for Solving the Advection-Diffusion Equation

[摘要] Up to tenth-order finite difference schemes are proposed in this paper to solve one-dimensional advection-diffusion equation. The schemes based on high-order differences are presented using Taylor series expansion. To obtain the solutions, up to tenth-order finite difference schemes in space and a fourth-order Runge-Kutta scheme in time have been combined. The methods are implemented to solve two problems having exact solutions. Numerical experiments have been conducted to demonstrate the efficiency and high-order accuracy of the current methods. The techniques are seen to be very accurate in solving the advection-diffusion equation for Pe ≤ 5 . The produced results are also seen to be more accurate than some available results given in the literature.

[学科分类] 计算数学

[关键词] Advection-Diffusion Equation;Contaminant Transport;High-order Finite Difference Schemes;Runge-Kutta