A Simplified Model of the Wave Generation Due to Train-Tunnel Entry

Kurzfassung

The compression wave generated when a high-speed train cnters a tunnel at Mach numbers smaller than 0.4 can be described in good approximation by a linear theory of an inviscid fluid. The wave equation for the acoustic potential becomes the governing equation. lt is solved by a three dimensional boundary elcment method in time domain which forces a vanishing normal component of the velocity at the tunnel wall. lt is assumed that the elements arc compact in time. This leads to a linear equation in which a special matrix-vector multiplication has to be evaluatcd for every time-step. The aim is to crcate a fast method which sets as few constraints on the geometry as possible but nevertheless gives an accurate description of the wave propagation. ln a first stcp the elements are assumed to bc rectangles and an infinitely thin cylindric tube of finite length is taken as the geometry of the tunnel. The train is modeled by a single moving mass source of monopole type. lt defines a semi-infinitc body whose shape slightly changes when entcring the tunnel. The results of this simple model along with the comparison with analytical solutions and experimental data are shown and discussed.