Modified nonequilibrium molecular dynamics for fluid flows with energy conservation

Abstract

The nonequilibrium molecular dynamics generated by the SLLOD algorithm [so called due to its association with the DOLLS tensor algorithm (D. J. Evans and G. P. Morriss, Statistical Mechanics of Nonequilibrium Liquids (Academic, New York, 1990)] for fluid flow is considered. It is shown that, in the absence of time-dependent boundary conditions (e.g., shearing boundary conditions via explicit cell dynamics or Lees–Edwards boundary conditions), a conserved energy, H exists for the equations of motion. The phase space distribution generated by SLLOD dynamics can be explicitly derived from H. In the case of a fluid confined between two immobile boundaries undergoing planar Couette flow, the phase space distribution predicts a linear velocity profile, a fact which suggests the flow is field driven rather than boundary driven. For a general flow in the absence of time-dependent boundaries, it is shown that the SLLOD equations are no longer canonical in the laboratory momenta, and a modified form of the SLLOD dynamics is presented which is valid arbitrarily far from equilibrium for boundary conditions appropriate to the flow. From an analysis of the conserved energy for the new SLLOD equations in the absence of time-dependent boundary conditions, it is shown that the correct local thermodynamics is obtained. In addition, the idea of coupling each degree of freedom in the system to a Nosé–Hoover chain thermostat is presented as a means of efficiently generating the phase space distribution.

Derivation of Langevin dynamics in a nonzero background flow field

“…Several strategies have been proposed to sample molecular systems under nonzero flow: for example, the SLLOD and g-SLLOD equations of motion [8,9,26,27] or dissipative particle dynamics [24]. Typically, these are used in conjunction with consistent boundary conditions such as the LeesEdwards boundary conditions [9] in the case of shear flow or the Kraynik-Reinelt boundary conditions [25] for elongational flow.…”

Rheological and structural studies of liquid decane, hexadecane, and tetracosane under planar elongational flow using nonequilibrium molecular-dynamics simulations

“…The p-SLLOD algorithm was originally proposed by Tuckerman et al, 12 and later derived by Edwards and Dressler 13 through a fundamental investigation of the canonical structure of the evolution equations under a completely Hamiltonian perspective. In the authors' recent paper, 11 the fundamental correctness of the p-SLLOD algorithm was further demonstrated through a detailed analysis of all the existing NEMD algorithms ͑DOLLS, SLLOD, and p-SLLOD͒.…”

Effective confinement as origin of the equivalence of kinetic temperature and fluctuation-dissipation ratio in a dense shear-driven suspension

“…Since dynamics slows down dramatically and the time-scale separation between vibrations and long-lived particle displacements becomes even more pronounced we expect that our results extend into the supercooled regime. While we have employed stochastic dynamics one might speculate that our results also hold in systems governed by deterministic dynamics such as the SLLOD equations of motion [39] as employed in Ref. [21].…”