Computational fluctuating fluid dynamics

Abstract

Abstract. This paper describes the extension of a recently developed numerical solver for the LandauLifshitz Navier-Stokes (LLNS) equations to binary mixtures in three dimensions. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by using white-noise fluxes. These stochastic PDEs are more complicated in three dimensions due to the tensorial form of the correlations for the stochastic fluxes and in mixtures due to couplings of energy and concentration fluxes (e.g., Soret effect). We present various numerical tests of systems in and out of equilibrium, including timedependent systems, and demonstrate good agreement with theoretical results and molecular simulation.Mathematics Subject Classification. 35R60, 60H10, 60H35, 82C31, 82C80.

Fluctuating hydrodynamics of multi-species reactive mixtures

“…The fluid was taken to be a dilute binary mixture of hard-sphere gases, using kinetic theory formulae for the transport coefficients [39]. In CGS units, the species diameters are σ 1 = 2.58 · 10 −8 and σ 2 = 3.23 · 10 −8 , and m 1 = 6.64 · 10 −23 .…”

Proper orthogonal decomposition of atomistic flow simulations

“…Applicability of WPOD should be further explored in fluctuating hydrodynamics [18][19][20] and atomistic simulations of materials.…”

Fluctuating hydrodynamics for a rarefied gas based on extended thermodynamics

“…a(k, t) is a Gaussian white random force vector with 2 components. As is well known, the general solution for the variable y can be easily obtained explicitly by using the eigenvalues λ 1 and λ 2 of the matrix M , and the corresponding eigenvectors [u 1 , 1] T and [u 2 , 1] T : · C 1 e −λ 1 t C 2 e −λ 2 t (22) with integration constants C 1 and C 2 that are determined by the initial condition at t = 0, and…”

“…Numerical analyses of the fluctuations by using the theory have been made extensively [16][17][18][19][20][21][22]. The fluctuating-hydrodynamic approach can also contribute to the study of fluctuations in nonequilibrium states [11,23,24].…”