Lifting in equation-free methods for molecular dynamics simulations of dense fluids

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June 2009, 11(4): 855-874. doi: 10.3934/dcdsb.2009.11.855

Lifting in equation-free methods for molecular dynamics simulations of dense fluids

Yves Frederix ^1, , Giovanni Samaey ^1, , Christophe Vandekerckhove ^1, , Ting Li ^2, , Erik Nies ^2, and Dirk Roose ^1,

1.	Department of Computer Science, K.U.Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium, Belgium, Belgium, Belgium
2.	Polymer Research Division, Department of Chemistry, K.U.Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium, Belgium

Received July 2008 Revised October 2008 Published April 2009

Abstract
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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 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 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 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 (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.

Keywords: Multiscale, equation-free, initialization, molecular dynamics., lifting.

Mathematics Subject Classification: Primary: 70G6.

Citation: Yves Frederix, Giovanni Samaey, Christophe Vandekerckhove, Ting Li, Erik Nies, Dirk Roose. Lifting in equation-free methods for molecular dynamics simulations of dense fluids. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 855-874. doi: 10.3934/dcdsb.2009.11.855

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