求解声波动方程的隐格式有限体积法

An implicit finite volume method for the acoustic wave equation

摘要:

为研究声传播问题,提出一种声波动方程的隐格式有限体积法,该方法将格点型有限体积法与Newmark格式相结合．模拟平面波的传播过程,对比分析隐格式有限体积法和文献中显格式有限体积法的精度、稳定性及计算消耗等方面的性能．数值结果表明:当λ／Δx≥10时,两种算法均能得到满足精度要求的解;采用无条件稳定的隐格式算法,当满足ω₀Δt≤0.3时,预测声压的相对峰值误差＜1％;当采用相同时间、空间步长时,隐格式算法精度高于显格式算法;隐格式算法对吸收边界的处理精度高于显格式算法,但对全反射边界的处理精度低于显格式算法;两种算法内存消耗比较接近,显格式算法的CPU耗时较少．

Abstract:

An implicit finite volume method (FVM) with Newmark scheme is proposed for the sound propagation problem, and it is used to simulate the propagation of the plane wave. By comparing to the results from the FVM with that of explicit central difference algorithm, the numerical error, stability and computational consumption are analyzed. It is shown that both methods can acquire accurate numerical solutions when λ／Δx≥10. The relative peak error of the implicit scheme is less than 1％ when ω₀Δt≤0.3. With the same time step and spatial step, the numerical result of the implicit scheme agrees better with the exact result. The implicit method treats the absorbing boundary condition more accurate than the explicit method, but it is reverse for the total reflecting boundary condition. The two methods consume similar memory and the explicit method consumes less CPU time.