A Crank-Nicolson unconditionally stable method for solving 2D acoustic wave equations

被引：0
|
作者：
Fu Z. [1 ]
Shi L. [1 ]
Huang Z. [1 ]
Fu S. [1 ]
机构：
[1] National Key Laboratory on Electromagnetic Environmental Effects and Electro-optical Engineering, PLA University of Science and Technology, Nanjing
来源：
Shi, Lihua (lihuashi@aliyun.com) | 1600年 / Chinese Vibration Engineering Society卷 / 36期
关键词：
Acoustic wave equation; Crank-Nicolson method; Non-uniform grid; Unconditionally stable;
D O I：
10.13465/j.cnki.jvs.2017.17.013
中图分类号：
学科分类号：
摘要：
Considering the constraint of Courant-Friedrich-Levy (CFL) stability condition, it is time-consuming to solve the one-order velocity-pressure acoustic wave equation with the conventional finite-difference time domain (FDTD) method, especially, to analyze fine structure problems. Here, Crank-Nicolson (CN) method was introduced in finite difference simulation, the acoustic wave equation's CN difference scheme was obtained. Based on Von Neuman method, the unconditional stability condition of CN method for acoustic wave equations was derived. With the proposed method, the time step was not restricted by the CFL stability condition any more. Meanwhile, the non-uniform grid technology was used to generate mesh grids to further save internal memory and improve simulation efficiency. In simulation tests, a 2-dimentional multi-layer fine structure's sound propagation model was established. Through comparing the simulation test results with those using the traditional FDTD method, the effectiveness of the proposed method was verified. © 2017, Editorial Office of Journal of Vibration and Shock. All right reserved.
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页码：79 / 84
页数：5
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