High-order compact boundary value method for the solution of unsteady convection-diffusion problems
High-order compact boundary value method for the solution of unsteady convection-diffusion problems
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DOI：
10.1016/j.matcom.2008.04.015
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发表时间：
2008-12
期刊：
影响因子：
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通讯作者：
M. Dehghan;A. Mohebbi
中科院分区：
文献类型：
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作者：
M. Dehghan;A. Mohebbi
本文提出了一类新的求解二维非定常对流扩散方程的高精度方法。这些技术是基于线的方法的方法。我们应用一个紧凑的四阶有限差分近似的离散空间导数和四阶边值方法的时间积分的线性常微分方程组。所提出的方法在空间和时间变量都具有四阶精度。由于边值方法具有良好的稳定性，该方法也是无条件稳定的。数值结果表明，四阶紧致差分近似和四阶边值方法是求解这类问题的有效算法。
In this paper, we propose a new class of high-order accurate methods for solving the two-dimensional unsteady convection–diffusion equation. These techniques are based on the method of lines approach. We apply a compact finite difference approximation of fourth order for discretizing spatial derivatives and a boundary value method of fourth order for the time integration of the resulted linear system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables. Also this method is unconditionally stable due to the favorable stability property of boundary value methods. Numerical results obtained from solving several problems include problems encounter in many transport phenomena, problems with Gaussian pulse initial condition and problems with sharp discontinuity near the boundary, show that the compact finite difference approximation of fourth order and a boundary value method of fourth order give an efficient algorithm for solving such problems.