Introducing a moving load in a simulation in time over a truncated unbounded domain

Abstract

When using Finite Element methods to solve wave propagation problems, the spatial domain must be truncated at a finite distance. This can be done using absorbing boundary conditions or layers, which effectively inhibit the reflection of outgoing waves back into the computational domain. They cannot however handle moving loads coming from outside of the (truncated) computational domain, for which some incoming waves must be allowed. After illustrating this fact, this paper proposes a technique to introduce such moving loads in time simulations over finite size domains. This technique involves the introduction of appropriate initial conditions within the computational domain. In general, these initial conditions can be computed numerically, and possibly re-used for various configurations. The interest of the method is illustrated on industrial cases of interest for the railway community.