A high-order Padé ADI method for unsteady convection-diffusion equations
A high-order Padé ADI method for unsteady convection-diffusion equations
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DOI：
10.1016/j.jcp.2005.10.001
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
D. You
中科院分区：
文献类型：
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作者：
D. You
提出了一种计算非定常对流扩散方程的高阶交替方向隐式（ADI）方法。通过使用四阶Padé格式进行空间导数，该格式在空间上具有四阶精度，在时间上具有二阶精度。求解过程由许多三对角矩阵运算组成，这使得计算成本有效。该方法无条件稳定，并且比标准二阶ADI方法[D.W. Peaceman, H.H. Rachford Jr.，抛物线和椭圆微分方程的数值解，工业与应用数学学会杂志 3 (1959) 28–41] 和 Karaa 和 Zhang 的四阶 ADI 方案 [解决非稳态对流扩散问题的高阶 ADI 方法，计算物理学杂志 198 (2004) 1–9]。
A high-order alternating direction implicit (ADI) method for computations of unsteady convection–diffusion equations is proposed. By using fourth-order Padé schemes for spatial derivatives, the present scheme is fourth-order accurate in space and second-order accurate in time. The solution procedure consists of a number of tridiagonal matrix operations which make the computation cost effective. The method is unconditionally stable, and shows higher accuracy and better phase and amplitude error characteristics than the standard second-order ADI method [D.W. Peaceman, H.H. Rachford Jr., The numerical solution of parabolic and elliptic differential equations, Journal of the Society of Industrial and Applied Mathematics 3 (1959) 28–41] and the fourth-order ADI scheme of Karaa and Zhang [High order ADI method for solving unsteady convection–diffusion problem, Journal of Computational Physics 198 (2004) 1–9].