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Full-Text Articles in Physical Sciences and Mathematics
Low Mach Number Fluctuating Hydrodynamics Of Diffusively Mixing Fluids, Aleksandar Donev, Andy J. Nonaka, Yifei Sun, Thomas Fai, Alejandro Garcia, John B. Bell
Low Mach Number Fluctuating Hydrodynamics Of Diffusively Mixing Fluids, Aleksandar Donev, Andy J. Nonaka, Yifei Sun, Thomas Fai, Alejandro Garcia, John B. Bell
Alejandro Garcia
We formulate low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations eliminate the fast isentropic fluctuations in pressure associated with the propagation of sound waves by replacing the equation of state with a local thermodynamic constraint. We demonstrate that the low Mach number model preserves the spatio-temporal spectrum of the slower diffusive fluctuations. We develop a strictly conservative finite-volume spatial discretization of the low Mach number fluctuating equations in both two and three dimensions. We construct several explicit Runge-Kutta temporal integrators that strictly maintain the …
On The Accuracy Of Explicit Finite-Volume Schemes For Fluctuating Hydrodynamics, Aleksandar Donev, Eric Vanden-Eijnden, Alejandro Garcia, John B. Bell
On The Accuracy Of Explicit Finite-Volume Schemes For Fluctuating Hydrodynamics, Aleksandar Donev, Eric Vanden-Eijnden, Alejandro Garcia, John B. Bell
Alejandro Garcia
This paper describes the development and analysis of finite-volume methods for the Landau–Lifshitz Navier–Stokes (LLNS) equations and related stochastic partial differential equations in fluid dynamics. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by the addition of white noise fluxes whose magnitudes are set by a fluctuation-dissipation relation. Originally derived for equilibrium fluctuations, the LLNS equations have also been shown to be accurate for nonequilibrium systems. Previous studies of numerical methods for the LLNS equations focused primarily on measuring variances and correlations computed at equilibrium and for selected nonequilibrium flows. In this paper, we introduce a more systematic approach …
A Hybrid Particle-Continuum Method For Hydrodynamics Of Complex Fluids, Alejandro Garcia, Aleksandar Donev, John B. Bell, Berni Alder
A Hybrid Particle-Continuum Method For Hydrodynamics Of Complex Fluids, Alejandro Garcia, Aleksandar Donev, John B. Bell, Berni Alder
Alejandro Garcia
A previously developed hybrid particle-continuum method [J. B. Bell, A. Garcia, and S. A. Williams, Multiscale Model. Simul., 6 (2008), pp. 1256–1280] is generalized to dense fluids and two- and three-dimensional flows. The scheme couples an explicit fluctuating compressible Navier–Stokes solver with the isotropic direct simulation Monte Carlo (DSMC) particle method [A. Donev, A. L. Garcia, and B. J. Alder, J. Stat. Mech. Theory Exp., 2009 (2009), article P11008]. To achieve bidirectional dynamic coupling between the particle (microscale) and continuum (macroscale) regions, the continuum solver provides state-based boundary conditions to the particle subdomain, while the particle solver provides flux-based boundary …
Algorithm Refinement For Fluctuating Hydrodynamics, Alejandro Garcia, Sarah Williams, John B. Bell
Algorithm Refinement For Fluctuating Hydrodynamics, Alejandro Garcia, Sarah Williams, John B. Bell
Alejandro Garcia
This paper introduces an adaptive mesh and algorithm refinement method for fluctuating hydrodynamics. This particle-continuum hybrid simulates the dynamics of a compressible fluid with thermal fluctuations. The particle algorithm is direct simulation Monte Carlo (DSMC), a molecular-level scheme based on the Boltzmann equation. The continuum algorithm is based on the Landau–Lifshitz Navier–Stokes (LLNS) equations, which incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. It uses a recently developed solver for the LLNS equations based on third-order Runge–Kutta. We present numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate dynamic adaptive refinement by the …