Numerical local time stepping strategies for transient statistical energy analysis

The linear system of ordinary differential equations in transient statistical energy analysis (TSEA) is usually solved by means of a forward Euler finite difference strategy. The numerical stability of this scheme poses restrictions on the maximum allowable time step in the simulations. However, there also exist lower limits for the time step size because power spends a finite amount of time to travel across a subsystem, depending on its mean free path and group velocity. Actually, in a practical situation subsystems will evolve at different time scales and if this is not taken into account, errors may occur, for instance, in the prediction of energy decay curves. It is proposed to partially mitigate this problem by resorting to local time stepping finite difference strategies in which groups of subsystems can evolve in TSEA at different time scales.