Element Differential Method for Computational Acoustics in Time Domain

In this paper, a new robust numerical method, named element differential method (EDM), is developed to solve computational acoustic problems in time domain. The key aspect of the method is the direct differentiation of shape functions of the isoparametric elements used to characterize the geometry and physical variables, which can be utilized to evaluate the spatial partial derivatives of the physical variables appearing in the governing equations and boundary conditions. Moreover, a unique collocation technique is proposed to form the system of equations, in which the governing equation is collocated at internal nodes of elements and the acceleration equilibrium equation is collocated at interface nodes between elements and outer surface nodes. EDM is a strong-form numerical method that doesn't require a variational principle or a control volume to set up the computational scheme, and no integration is performed. Based on the Newmark difference technique, a time marching solution scheme is developed for solving the time-dependent system of equations. For the point sound source expressed in terms of the Dirac function, a sound source density function is proposed to approximate the point sound source to make it handleable in EDM. Three numerical examples are given to demonstrate the correctness and application potential of the developed method.