A staggered time integrator for the linear acoustic wave equation using the Jacobi-Anger expansion

• Published in: Journal of computational physics Vol. 416; p. 109489
• Main Authors: Lee, Jaejoon, Park, Yoonseo, Park, Hyunseo, Shin, Changsoo, Chung, Wookeen
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.09.2020; Elsevier Science Ltd
• Subjects: Accuracy; Acoustic waves; Computational efficiency; Computational physics; Computer simulation; Computing costs; Design parameters; Domains; Jacobi-Anger expansion; Lax-Wendroff method; Linear acoustic wave equation; Mathematical models; Pseudospectral method; Spectral methods; Staggered time integrator; Strategy; Trigonometric functions; Wave equations; Wave propagation; Wavelengths; Jacobi-Anger expansion; Linear acoustic wave equation; Staggered time integrator; Pseudospectral method
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2020.109489

•Two-stage staggered time integrator with the Jacobi-Anger expansion is introduced.•The method can be twice as faster than the Taylor expansion based time integrator.•Accuracy condition is obtained to bound error of the solution within a preset level.•Optimal strategy for the method is to use allowable maximum time step length. In this study, we introduce a staggered time integrator with the Fourier pseudospectral method to solve the first-order linear wave equation, which is accelerated by using the Jacobi-Anger expansion. The proposed method can reduce the computational cost by approximately half compared to the scheme whose temporal order of accuracy is extended by the Lax-Wendroff method under the equivalent modeling conditions, such as time step length, grid interval and maximum wave propagation speed. This is because the Jacobi-Anger expansion can effectively approximate the sinusoidal function, which in our case is the sine function in the wavenumber domain. Based on the wavenumber domain analysis of the proposed method, a strategy to optimally design the simulation parameters to maintain a preset level of accuracy is also introduced. According to the strategy, as the time step length increases, not only the computational cost of the simulation is reduced, but also the accuracy of the numerical solution is improved. Numerical simulations are also performed by using both homogeneous and heterogeneous models to validate the introduced strategy, which supports the practicality of the proposed method.