A Crank-Nicolson Unconditionally Stable Method for Solving 2D Acoustic Wave Equation
Fu Zhi-Kai Shi Li-Hua Huang Zheng-Yu Fu Shang-Chen
National Key Laboratory on Electromagnetic Environmental Effects and Electro-optical Engineering, PLA University of Science and Technology, Nanjing 210007, China.
Considering the restriction of the Courant-Friedrich-Levy (CFL) stability condition, it is time-consuming to solve the one-order velocity-pressure acoustic wave equation by conventional finite-difference time domain (FDTD) method, especially in analyzing the fine structure problems. This paper introduces the Crank-Nicolson (CN) method to solve the acoustic wave equation. Based on Von Neuman method, the unconditional stability of the CN method of the acoustic wave equation is proved. With the proposed method, the time step will not be restricted by the CFL stability condition any more. Meanwhile, the non-uniform grid technology is used to generate the mesh grid, which further saves the CPU memory and improves the efficiency. In the simulation, a 2-dimentional multi-layers model with fine structure is established. By comparing the simulation results between the traditional FDTD method and the CN method, the effectiveness of the proposed method is proved.
富志凯，石立华,黄正宇，付尚琛. 二维声波方程的Crank-Nicolson无条件稳定方法研究[J]. 振动与冲击, 2017, 36(17): 79-84.
Fu Zhi-Kai Shi Li-Hua Huang Zheng-Yu Fu Shang-Chen . A Crank-Nicolson Unconditionally Stable Method for Solving 2D Acoustic Wave Equation. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(17): 79-84.
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