Issues in modeling fluctuating hydrodynamics

Alejandro Garcia

San José State University and Berkeley Lab

Thursday, Aug 15, 2024, 3:00 pm MT
DSRC Room 2A305

JOIN THE WEBINAR:

Abstract

The intrinsic thermal motion of the molecules in a fluid result in microscopic fluctuations that are well-understood at thermodynamic equilibrium. For a fluid in a nonequilibrium state, such as in the presence of gradients of temperature or concentration, these hydrodynamic fluctuations are qualitatively different, potentially becoming macroscopic in amplitude and length scale.

Thermal fluctuations can be modeled accurately using a modification of the Navier-Stokes conservation equations that includes a stochastic forcing, as was originally proposed by Landau and Lifshitz. In this fluctuating hydrodynamics (FHD) formulation, a stochastic flux is added to each dissipative flux associated with the transport of species mass, momentum and energy densities in a manner that satisfies the fluctuation-dissipation balance. The framework of FHD has been useful in understanding the behavior of fluids in various nonequilibrium conditions, but theoretical calculations have been feasible only with simplifying assumptions.

This talk will review the numerical methods for simulations based on the FHD equations for both compressible and incompressible flows. First, the basic ideas will be illustrated using the one-dimensional stochastic heat equation, which can be solved analytically. The concepts will then be extended to the full hydrodynamic equations with multiple species and chemical reactions. Finally, a selection of examples will be reviewed including gas-phase membranes, electrolyte solutions, wetting instabilities, and turbulence.

About: Professor Alejandro Garcia teaches in the Department of Physics and Astronomy at San Jose State and is an affiliate of the Center for Computational Sciences and Engineering at Berkeley Lab. He has published over 100 professional articles in the fields of computational physics, statistical mechanics, and fluid mechanics. Dr. Garcia is the author of the textbooks, "Numerical Methods for Physics" and "Essentials of Modern Thermodynamics." As physics consultant for DreamWorks Animation, he has screen credit on: "Madagascar 3: Europe's Most Wanted", "Mr. Peabody and Sherman", and "Trolls."