Simplified modelling of a thermal bath, with application to a fluid vortex system

Svetlana Dubinkina*, Jason Frank, Ben Leimkuhler

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


Based on the thermodynamic concept of a reservoir, we investigate a computational model for interaction with unresolved degrees of freedom (a thermal bath). We assume that a finite restricted system can be modelled by a generalized canonical ensemble, described by a density which is a smooth function of the energy of the restricted system. A thermostat is constructed to continuously perturb the resolved dynamics, while leaving the desired equilibrium distribution invariant. We build on a thermostatting framework developed and tested in the setting of molecular dynamics, using stochastic perturbations to control (and stabilize) the invariant measure. We also apply these techniques in the setting of a simplified point vortex flow on a disc, in which a modified Gibbs distribution (modelling a finite, rather than infinite, bath of weak vortices) provides a regularizing formulation for restricted system dynamics. Numerical experiments, effectively replacing many vortices by a few artificial degrees of freedom, are in excellent agreement with the two-scale simulations of Bühler.

Original languageEnglish
Pages (from-to)1882-1901
Number of pages20
JournalMultiscale Modeling and Simulation
Issue number5
Publication statusPublished - 1 Dec 2010
Externally publishedYes


  • Bulgac-Kusnezov
  • Generalized canonical ensembles
  • Nosé dynamics
  • Point vortex fluid
  • Thermostat methods
  • Unresolved dynamics


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