Numerical Local Time Stepping Solutions for Transient Statistical Energy Analysis

Abstract

Subsystem energies evolve in transient statistical energy analysis (TSEA) according to a linear system of ordinary differential equations (ODEs), which is usually numerically solved by means of the forward Euler finite difference scheme. Stability requirements pose limits on the maximum time step size to be used. However, it has been recently pointed out that one should also consider a minimum time step limit, if time independent loss factors are to be assumed. This limit is based on the subsystem internal time scales, which rely on their characteristic mean free paths and group velocities. In some cases, these maximum and minimum limits become incompatible, leading to a blow up of the forward Euler solution. It is proposed to partially mitigate this problem by resorting to a local time-stepping finite difference strategy. Subsystems are grouped into sets characterized by different time step sizes and evolve according to them.