Simplified modelling of a thermal bath, with application to a fluid vortex system
(2010) Multiscale Modeling & Simulation: a S I A M Interdisciplinary Journal — Vol. 8, n° 5, p. 1882-1901 (2010)
Files
Ther_09.pdf
Restricted Access - Adobe PDF
- 5.53 MB
Details
- Authors
- Abstract
- 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. © 2010 Society for Industrial and Applied Mathematics.
- Affiliations
Citations
Dubinkina, S., Frank, J., & Leimkuhler, B. (2010). Simplified modelling of a thermal bath, with application to a fluid vortex system. Multiscale Modeling & Simulation: a S I A M Interdisciplinary Journal, 8(5), 1882-1901. https://doi.org/10.1137/100795152 (Original work published 2010)