A simplified model of the wave generation due to train-tunnel entry

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 non-viscous 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 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 but nevertheless gives an accurate description of the wave propagation. In a first step the elements are assumed to be rectangles. An infinitely thin cylindric tube of finite length is taken as a first 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 will be presented and discussed at the conference.