A high order finite difference method with Richardson extrapolation for 3D convection diffusion equation

作者：Ma, Yuezhen; Ge, Yongbin^*

来源：Applied Mathematics and Computation, 2010, 215(9): 3408-3417.

DOI：10.1016/j.amc.2009.10.035

• 3D convection diffusion equation
• High order compact scheme
• Richardson extrapolation
• ADI method
• Finite difference method

In this paper, we extend the Sun and Zhang's [24] work on high order finite difference method, which is based on the Richardson extrapolation technique and an operator interpolation scheme for the one and two dimensional steady convection diffusion equations to the three dimensional case. Firstly, we employ a fourth order compact difference scheme to get the fourth order accurate solution on the fine and the coarse grids. Then, we use the Richardson extrapolation technique by combining the two approximate solutions to get a sixth order accurate solution on coarse grid. Finally, we apply an operator interpolation scheme to achieve the sixth order accurate solution on the fine grid. During this process, we use alternating direction implicit (ADI) method to solve the resulting linear systems. Numerical experiments are conducted to verify the accuracy and effectiveness of the present method.

• 出版日期2010-1-1
• 单位宁夏大学