High-quality and efficient means of transport is of high priority in the modern society. Railway traffic is environment friendly and economically very competitive for both freight and personal transports at mid-range distances. Although the railway technology has been improved substantially during the last decades, generated vibrations still impose annoyances to the surroundings environment and leads to deterioration of the track structure.
To understand the physical phenomena and propose countermeasures/improvements, simulation tools to perform computations of the entire dynamical system including subground, track structure and the railway vehicle has been developed. In particular, large effort has been devoted to the special wave propagation problem related to high-speed trains running at soft ground materials. As the speed of the train approaches and exceeds the natural (Rayleigh) wave propagation velocity of the ground material, shock waves similar to sonic boom originates from the onrushing train. The problem area contains several computational challenges since it impose techniques to handle non-reflecting boundaries[
], time integration of large-scale problems, non-linear material response etc.
Efficient solvers based on a combination of multigrid[
], error estimations and adaptive refinement has been developed to reach acceptable execution times. The solution time is substantially reduced compared to conventional implicit solvers based on factorization. Moreover, indefinite system from the Lagrange multiplier approach to handle constraint equations imposes additional preconditioning to guarantee convergence and reducing the number of iterations.
In the paper a number of numerical examples from railway applications are presented. Results from computation where the train is represented as a collection of moving loads as well as a multi body system with complete train-track interaction are demonstrated.