A High-Order Finite-Difference Algorithm for the Analysis of Standing Acoustic Waves of Finite but Moderate Amplitude

A numerical formulation for modelling standing acoustic waves of finite but moderate amplitude is presented. A thermoviscous fluid contained in a one-dimensional tube with rigid walls is considered. The fluid is initially at rest and is excited by means of a harmonic piston. A second-order wave equation for viscous and homogeneous fluids is used. The perturbation method is employed. The numerical simulation is carried out by a multi-time-step, implicit, six-point finite-difference scheme of high order in the time domain. Displacement and pressure waveforms and distributions are presented. Numerical results are validated by comparison with an analytical model. The numerical scheme is illustrated with several examples.