Numerical Simulation of Train-Tunnel Entry Using a BEM in Time Domain

Abstract

The compression wave generated when a high-speed train enters a tunnel at Mach numbers smaller than 0.4 can be described in good approximation by a linear theory of a inviscid compressible fluid. The wave equation for the acoustic potential becomes the governing equation. It is solved by a three dimensional boundary element method in time domain which forces a vanishing normal component of the velocity at the tunnel wall. It is assumed that the elements are compact in time. This leads to a linear equation in which a special matrix-vector multiplication has to be evaluated for every time-step. The aim is to create a fast method which sets as few constraints on the geometry as possible while still beeing accurate enough to be used as a first estimate of the occuring wave propagation. In a first step the elements are assumed to be rectangles and a cylinder of finite length with infinitely thin walls is taken as the geometry of the tunnel. The train is modeled by a single moving mass source of monopole type. It defines a semi-infinite body whose shape slightly changes when entering the tunnel. The results of this simple model along with the comparison with analytical solutions and experimental data are shown and discussed.