19 research outputs found
Algorithm Refinement for Fluctuating Hydrodynamics
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 computation of a moving shock wave. Mean system behavior and second moment statistics of our simulations match theoretical values and benchmarks well. We find that particular attention should be paid to the spectrum of the flux at the interface between the particle and continuum methods, specifically for the nonhydrodynamic (kinetic) time scales
Algorithm Refinement for Fluctuating Hydrodynamics
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 al
Meshfree method for the stochastic Landau-Lifshitz Navier-Stokes equations
The current study aimed to develop a meshfree Lagrangian particle method for the Landau-Lifshitz Navier-Stokes (LLNS) equations. The LLNS equations incorporate thermal fluctuation into macroscopic hydrodynamics by addition of white noise fluxes whose magnitudes are set by a fluctuation-dissipation theorem. Moreover, the study focuses on capturing correct variance and correlation computed at equilibrium flows, which are compared with available theoretical values and found very good agreement
A Thermodynamically-Consistent Non-Ideal Stochastic Hard-Sphere Fluid
A grid-free variant of the Direct Simulation Monte Carlo (DSMC) method is
proposed, named the Isotropic DSMC (I-DSMC) method, that is suitable for
simulating dense fluid flows at molecular scales. The I-DSMC algorithm
eliminates all grid artifacts from the traditional DSMC algorithm; it is
Galilean invariant and microscopically isotropic. The stochastic collision
rules in I-DSMC are modified to yield a non-ideal structure factor that gives
consistent compressibility, as first proposed in [Phys. Rev. Lett. 101:075902
(2008)]. The resulting Stochastic Hard Sphere Dynamics (SHSD) fluid is
empirically shown to be thermodynamically identical to a deterministic
Hamiltonian system of penetrable spheres interacting with a linear core pair
potential, well-described by the hypernetted chain (HNC) approximation. We
apply a stochastic Enskog kinetic theory for the SHSD fluid to obtain estimates
for the transport coefficients that are in excellent agreement with particle
simulations over a wide range of densities and collision rates. The fluctuating
hydrodynamic behavior of the SHSD fluid is verified by comparing its dynamic
structure factor against theory based on the Landau-Lifshitz Navier-Stokes
equations. We also study the Brownian motion of a nano-particle suspended in an
SHSD fluid and find a long-time power-law tail in its velocity autocorrelation
function consistent with hydrodynamic theory and molecular dynamics
calculations.Comment: 30 pages, revision adding some clarifications and a new figure. See
also arXiv:0803.035
Predictive Scale-Bridging Simulations through Active Learning
Throughout computational science, there is a growing need to utilize the
continual improvements in raw computational horsepower to achieve greater
physical fidelity through scale-bridging over brute-force increases in the
number of mesh elements. For instance, quantitative predictions of transport in
nanoporous media, critical to hydrocarbon extraction from tight shale
formations, are impossible without accounting for molecular-level interactions.
Similarly, inertial confinement fusion simulations rely on numerical diffusion
to simulate molecular effects such as non-local transport and mixing without
truly accounting for molecular interactions. With these two disparate
applications in mind, we develop a novel capability which uses an active
learning approach to optimize the use of local fine-scale simulations for
informing coarse-scale hydrodynamics. Our approach addresses three challenges:
forecasting continuum coarse-scale trajectory to speculatively execute new
fine-scale molecular dynamics calculations, dynamically updating coarse-scale
from fine-scale calculations, and quantifying uncertainty in neural network
models
On the Suppression and Distortion of Non-Equilibrium Fluctuations by Transpiration
A fluid in a non-equilibrium state exhibits long-ranged correlations of its
hydrodynamic fluctuations. In this article, we examine the effect of a
transpiration interface on these correlations -- specifically, we consider a
dilute gas in a domain bisected by the interface. The system is held in a
non-equilibrium steady state by using isothermal walls to impose a temperature
gradient. The gas is simulated using both direct simulation Monte Carlo (DSMC)
and fluctuating hydrodynamics (FHD). For the FHD simulations two models are
developed for the interface based on master equation and Langevin approaches.
For appropriate simulation parameters, good agreement is observed between DSMC
and FHD results with the latter showing a significant advantage in
computational speed. For each approach we quantify the effects of transpiration
on long-ranged correlations in the hydrodynamic variables
Computational fluctuating fluid dynamics
This paper describes the extension of a recently developed numerical solver for the Landau-Lifshitz 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 time-dependent systems, and demonstrate good agreement with theoretical results and molecular simulatio