A Compact High-Order Finite Difference Method for Unsteady Convection-Diffusion Equation
A Compact High-Order Finite Difference Method for Unsteady Convection-Diffusion Equation
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DOI：
10.1080/15502287.2012.660227
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发表时间：
2012-04
影响因子：
1.6
通讯作者：
Wenyuan Liao
中科院分区：
文献类型：
--
作者：
Wenyuan Liao
本文提出了一种求解非定常对流扩散方程的四阶紧致有限差分方法。我们首先将对流扩散方程转化为反应扩散方程，然后用紧凑的高阶方法进行求解。新方法是无条件稳定的，在时间和空间维度上都具有四阶精度。一维问题只需要三点模板，二维问题只需要五点模板。给出了两个数值算例，验证了数值方法的有效性和准确性。
In this paper, a fourth-order compact finite difference method is proposed to solve the unsteady convection-diffusion equation. We first transform the convection-diffusion equation to a reaction-diffusion equation, which is then solved by a compact high-order method. The new method is unconditionally stable and fourth-order accurate in both temporal and spatial dimensions. It requires only a three-point stencil for a one-dimensional problem and a five-point stencil for a two-dimensional problem. Two numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method.