Staggered Scheme for the Compressible Fluctuating Hydrodynamics of Multispecies Fluid Mixtures

TL;DR

This paper introduces a novel staggered grid numerical scheme for simulating non-isothermal, compressible, multispecies fluid mixtures with thermal fluctuations, improving accuracy and boundary condition handling over previous methods.

Contribution

The paper presents a staggered grid finite volume method for stochastic compressible Navier-Stokes equations, enhancing the accuracy of hydrodynamic fluctuation simulations in multispecies gases.

Findings

More accurate reproduction of equilibrium static structure factors.

Effective modeling of giant nonequilibrium fluctuations and Rayleigh-Taylor instability.

Excellent agreement with theoretical and DSMC results.

Abstract

We present a numerical formulation for the solution of non-isothermal, compressible, Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical method is the use of staggered grid momenta along with a finite volume discretization of the thermodynamic variables to solve the resulting stochastic partial differential equations. The key advantages of the numerical scheme are significantly simplified and compact discretization of the diffusive and stochastic momentum fluxes, and an unambiguous prescription of boundary conditions involving pressure. The staggered grid scheme more accurately reproduces the equilibrium static structure factor of hydrodynamic fluctuations in gas mixtures compared to a collocated scheme described previously in Balakrishnan \emph{et al.} [Phys. Rev. E 89, 013017 (2014)]. The numerical method is tested for ideal noble gases mixtures under various nonequilibrium conditions, such as applied thermal and concentration gradients, to assess the role of cross-diffusion effects, such as Soret and Dufour, on the long-ranged correlations of hydrodynamic fluctuations, which are also more accurately reproduced compared to the collocated scheme. We numerically study giant nonequilibrium fluctuations driven by concentration gradients, and fluctuation-driven Rayleigh-Taylor instability in gas mixtures. Wherever applicable, excellent agreement is observed with theory and measurements from the direct simulation Monte Carlo (DSMC) method.