On the dispersion, stability and accuracy of a compact higher-order finite difference scheme for 3D acoustic wave equation
On the dispersion, stability and accuracy of a compact higher-order finite difference scheme for 3D acoustic wave equation
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DOI：
10.1016/j.cam.2013.08.024
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发表时间：
2014-11
期刊：
影响因子：
--
通讯作者：
Wenyuan Liao
中科院分区：
文献类型：
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作者：
Wenyuan Liao
本文提出了一种低数值色散的四阶紧致差分格式来求解三维声波方程。Padé近似已被用来获得四阶精度在时间和空间维度，而交替方向隐式（ADI）技术已被用来降低计算成本。误差分析表明，该方法具有四阶精度，并通过数值算例得到了验证。我们还表明，所提出的方法是条件稳定的Courant-Friedrichs-Lewy（CFL）的条件，是与其他现有的有限差分格式。由于高阶精度，新方法被发现有效地抑制数值色散。
In this paper, we propose a compact fourth-order finite difference scheme with low numerical dispersion to solve the 3D acoustic wave equation. Padé approximation has been used to obtain fourth-order accuracy in both temporal and spatial dimensions, while the alternating direction implicit (ADI) technique has been used to reduce the computational cost. Error analysis has been conducted to show the fourth-order accuracy, which has been confirmed by a numerical example. We have also shown that the proposed method is conditionally stable with a Courant–Friedrichs–Lewy (CFL) condition that is comparable to other existing finite difference schemes. Due to the higher-order accuracy, the new method is found effective in suppressing numerical dispersion.