Title: Lifting in equation-free methods for molecular dynamics simulations of dense fluids
Authors: Frederix, Yves ×
Samaey, Giovanni
Vandekerckhove, Christophe
Li, Ting
Nies, Eric
Roose, Dirk #
Issue Date: Jun-2009
Publisher: Dept. of Mathematics, Southwest Missouri State University
Series Title: Discrete and Continuous Dynamical Systems B vol:11 issue:4 pages:855-874
Abstract: Within the context of multiscale computations, equation-free methods have been developed. In this approach, the evolution of a system is simulated on the macroscopic level while only a microscopic model is explicitly available. To this end, a \emph{coarse time stepper} for the macroscopic variables can be constructed, based on appropriately initialized microscopic simulations. In this paper, we investigate the initialization of the microscopic simulator using the macroscopic variables only (called \emph{lifting} in the equation-free framework) when the microscopic model is a molecular dynamics (MD) description of a mono-atomic dense fluid. We assume a macroscopic model to exist in terms of the lowest order velocity moments of the particle distribution (density, velocity and temperature). The major difficulty is to design a lifting operator that accurately reconstructs the physically correct state of the fluid (i.e., the higher order moments) at a reasonable computational cost. We construct a lifting operator, as well as a \emph{restriction} operator for the reverse mapping. For a simple model problem, we perform a systematic numerical study to assess the time scales on which the lifting errors disappear after reinitialization (\emph{healing}); we also examine the effects on the simulated macroscopic behavior. The results show that, although in some cases accurate initialization of the higher order moments is not crucial, in general a detailed study of the lifting operator is required.
ISSN: 1531-3492
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
Molecular Imaging and Photonics
Polymer Chemistry and Materials
× corresponding author
# (joint) last author

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