Acoustic calculations with the hybrid boundary element method in time domain

Abstract

The boundary element method (BEM) is an efficient tool for the calculation of acoustic wave propagation in fluids. Transient waves can be solved by either using a formulation in frequency domain along with an inverse Fourier transformation or a time domain formulation. To increase the efficiency for the solver and allow for an efficient coupling with finite element domains the symmetry of the system matrices is advantageous. If Hamilton's principle is used, a symmetric variational formulation can be established with the velocity potential as field variable. The single field principle is generalized as multifield principle as basis of a hybrid BEM for the calculation of acoustic fields in compressible fluids in time domain. The state variables are separated into boundary variables, which are approximated by piecewise polynomials and domain variables, which are approximated by a superposition of weighted fundamental solutions. In both approximations the time and space dependency is separated. This is why static fundamental solution can be used for the field approximation. The domain integrals are eliminated, respectively, transformed into boundary integrals and an equation of motion with symmetric mass and stiffness matrix is obtained, which can be solved by a direct time integration scheme or by mode superposition. The time derivative of the equation of motion leads to a formulation with pressure and acoustic flux on the boundary for an easier interpretation of the variables.