ICAMS / Interdisciplinary Centre for Advanced Materials Simulation


Thermal fluctuations in non-ideal gas lattice Boltzmann models

Date: 07.07.2010
Place: 19th Discrete Simulation of Fluid Dynamics, DSFD 2010, Rome, Italy

Markus Gross

We present recent progress on introducing thermal fluctuations into non-ideal gas lattice Boltzmann models. While LB models containing thermal fluctuations have already been introduced for simple fluids [Ladd, J. Fluid. Mech. 1994, Adhikari et al., EPL 2005], the present case of a liquid-vapor system has not been addressed previously. This problem becomes important, for example, for the simulation of capillary fluctuations or colloidal particles in the presence of liquid-vapor interfaces. Our approach is based on a square-gradient freeenergy
lattice Boltzmann method [Swift et al., PRL 1995]. The basic complication arises here due to the
underlying diffuse interface model, describing a fluid close to criticality. Therefore, in contrast to the ideal gas case, spatial correlations become important and give rise to a non-trivial density structure factor. We outline the physical background from continuum kinetic theory and discuss the hydrodynamic limit, comparing with the theory of fluctuating hydrodynamics of Landau-Lifshitz. We finally discuss the possible error sources due to discretization.

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