(untitled) (Communications in Computational Physics, 2008)
A multi-timescale algorithm is proposed for simulating time-dependent problems in micro- and nano- fluidics. The total simulation domain is spatially decomposed into two regions. Molecular dynamics is employed in the crucial interfacial regions and continuum hydrodynamics is adopted in the remaining bulk regions. The coupling is through “constrained dynamics” in an overlap region. Our time scheme is based on the time scale separation between the continuum macro time step and molecular micro time step. This allows the molecular dynamics during one macro time step to be treated as in quasi-steady state. Therefore, molecular simulation is only performed in two shorter time intervals. Through linear extrapolation of macroscopic velocities and re-initialization of particle configurations, we can significantly reduce the total computational cost. We demonstrate and discuss our time algorithm through hybrid simulation of channel flow driven by a sinusoidally moving top wall. Converging results are achieved for cases of large separation of time scale with much less computational cost than with the original hybrid simulation without time extrapolation.