Replica Time Integrators

Summary:

We developed a new class of time integrators, to be referred to as Replica Time Integrators (RTIs) that effectively bridges molecular dynamics and irreversible continuum thermodynamics. The essential idea behind RTIs consists of overlaying identical replicas of the coarse regions in the spatial discretization. The replicas are each run at its own slow time step and are out-of-phase with respect to each other by one fast time step. In this manner, the thermal phonons can be transmitted losslessly from the fine to the coarse-grained regions of the mesh. RTIs provide a natural and effective accounting device for tracking thermodynamic measures, such as heat and temperature, in the coarse-grained regions. In particular, RTIs permit heat to exit the coarse-grained regions and be transmitted into the regions of the mesh as a distribution of thermal phonons. These two fundamental properties combined ensure the two-way convertibility of heat and thermal phonons, a requirement for the accurate simulation of transport phenomena.