Space-time spectral element method solution for the acoustic wave equation and its dispersion analysis

Abstract

This paper presents the solution for the continuous space-time spectral element method (CSTSEM) based on Chebyshev polynomials for the acoustic wave equation. Acoustic wave propagation in various dimensions is simulated using quadrilateral, hexahedral, and tesseract elements. The convergence is studied for 1+1-dimensional wave propagation. The extended 2+1-and 3+1-dimensional wave equations are also numerically solved by CSTSEM and the dispersion characteristics are investigated. A fixed-! (! is the angular frequency) method is proposed for computing the dispersion of space-time coupled methods. CSTSEM is verified as a simple, practical isotropic algorithm with low dispersion and high accuracy.

Time domain room acoustic simulations using the spectral element method

“…The dispersive and dissipative properties of the SEM for wave problems have been widely studied. [52][53][54][55][56][57][58][59] A commonly used approach for analyzing these properties in finite element methods for wave problems uses eigenvalue analysis. The eigenvalue analysis has been used to prove that the SEM is non-dissipative for wave problems.…”

An accurate triangular spectral element method-based numerical simulation for acoustic problems in complex geometries

“…This feature makes SEM more accurate than FEM (which will be discussed later) and more efficient and convenient than FDM. There are some reports about successful implementation of SEM in CFD 9,10 and CAA 11,12 problems where high accuracy is required.…”