Investigation on Generalised Trapezoidal Differencing TimeMarching Scheme for Modelling of Acoustical Wave

Priscilla  Francesca; Wah Yen  Tey; Lit Ken  Tan; M.W.  Muhieldeen

Authors

Priscilla Francesca Department of Mechanical Engineering, Faculty of Engineering, UCSI University, Kuala Lumpur, Malaysia
Wah Yen Tey Takasago i-Kohza, Malaysia-Japan International Institute of Technology, Universiti Teknologi Malaysia, Kuala Lumpur, Malaysia
Lit Ken Tan International Center, Tokyo City University, 1-28-1, Tamazutsumi, Setagaya-ku, Tokyo, 158-8557, Japan
M.W. Muhieldeen Department of Mechanical Engineering, Faculty of Engineering, UCSI University, Kuala Lumpur, Malaysia

Keywords:

wave equation, explicit time-marching, implicit time-marching, first order time-marching, acoustic wave

Abstract

Generalised Trapezoidal Differencing Time-Marching (GTDTM) Scheme has been developed in this paper to solve non-linear wave equation for acoustical modelling. The method is indeed a combination between Euler explicit method and Euler implicit method. To investigate the computational accuracy for GTDTM, the explicit factor is reduced from 1 (fully explicit) to 0 (fully implicit). The results show that the lower the explicit factor, the propagated wave will be damped with a faster speed. As a remedy, the Courant number is reduced when the explicit factor is small. In fact, Euler implicit scheme is not an effective approach to solve the hyperbolic wave equation. However, the minimum Courant number required due to different explicit factor has been computed too for future implementation of GTDTM.