A High Order Compact ADI Method for Solving 3D Unsteady Convection Diffusion Problems
Applied and Computational Mathematics
Volume 7, Issue 1, February 2018, Pages: 1-10
Received: Dec. 3, 2017;
Accepted: Dec. 13, 2017;
Published: Jan. 12, 2018
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Yongbin Ge, Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, China
Fei Zhao, Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, China
Jianying Wei, Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, China
In this paper, we develop a rational high order compact alternating direction implicit (RHOC ADI) method for solving the three dimensional (3D) unsteady convection diffusion equation. The present scheme, based on the idea of the fourth order rational compact finite difference operator for the spatial discretization and the Crank-Nicolson method for the time discretization, is fourth order accurate in space and second order accurate in time. The solution procedure consists of a number of tridiagonal matrix operations, which makes the computation to be cost-effective. It is shown by means of the discrete Fourier analysis that this method is unconditionally stable. Three test problems are given to demonstrate the performance of the present method. The numerical results show that the present RHOC ADI scheme has higher accuracy and better phase and amplitude error characteristics than the classical second order Douglas-Gunn ADI method  and some high order compact ADI methods including the Karaa’s HOC ADI method , Cao and Ge’s HOC ADI method , and our previous exponential HOC ADI method .
A High Order Compact ADI Method for Solving 3D Unsteady Convection Diffusion Problems, Applied and Computational Mathematics.
Vol. 7, No. 1,
2018, pp. 1-10.
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