481 research outputs found
A new lattice Boltzmann model for interface reactions between immiscible fluids
In this paper, we describe a lattice Boltzmann model to simulate chemical reactions taking place at the interface between two immiscible fluids. The phase-field approach is used to identify the interface and its orientation, the concentration of reactant at the interface is then calculated iteratively to impose the correct reactive flux condition. The main advantages of the model is that interfaces are considered part of the bulk dynamics with the corrective reactive flux introduced as a source/sink term in the collision step, and, as a consequence, the model’s implementation and performance is independent of the interface geometry and orientation. Results obtained with the proposed model are compared to analytical solution for three different benchmark tests (stationary flat boundary, moving flat boundary and dissolving droplet). We find an excellent agreement between analytical and numerical solutions in all cases. Finally, we present a simulation coupling the Shan Chen multiphase model and the interface reactive model to simulate the dissolution of a collection of immiscible droplets with different sizes rising by buoyancy in a stagnant fluid
Mesoscopic simulation of diffusive contaminant spreading in gas flows at low pressure
Many modern production and measurement facilities incorporate multiphase
systems at low pressures. In this region of flows at small, non-zero Knudsen-
and low Mach numbers the classical mesoscopic Monte Carlo methods become
increasingly numerically costly. To increase the numerical efficiency of
simulations hybrid models are promising. In this contribution, we propose a
novel efficient simulation approach for the simulation of two phase flows with
a large concentration imbalance in a low pressure environment in the low
intermediate Knudsen regime. Our hybrid model comprises a lattice-Boltzmann
method corrected for the lower intermediate Kn regime proposed by Zhang et al.
for the simulation of an ambient flow field. A coupled event-driven
Monte-Carlo-style Boltzmann solver is employed to describe particles of a
second species of low concentration. In order to evaluate the model, standard
diffusivity and diffusion advection systems are considered.Comment: 9 pages, 8 figure
Inertial Coupling Method for particles in an incompressible fluctuating fluid
We develop an inertial coupling method for modeling the dynamics of
point-like 'blob' particles immersed in an incompressible fluid, generalizing
previous work for compressible fluids. The coupling consistently includes
excess (positive or negative) inertia of the particles relative to the
displaced fluid, and accounts for thermal fluctuations in the fluid momentum
equation. The coupling between the fluid and the blob is based on a no-slip
constraint equating the particle velocity with the local average of the fluid
velocity, and conserves momentum and energy. We demonstrate that the
formulation obeys a fluctuation-dissipation balance, owing to the
non-dissipative nature of the no-slip coupling. We develop a spatio-temporal
discretization that preserves, as best as possible, these properties of the
continuum formulation. In the spatial discretization, the local averaging and
spreading operations are accomplished using compact kernels commonly used in
immersed boundary methods. We find that the special properties of these kernels
make the discrete blob a particle with surprisingly physically-consistent
volume, mass, and hydrodynamic properties. We develop a second-order
semi-implicit temporal integrator that maintains discrete
fluctuation-dissipation balance, and is not limited in stability by viscosity.
Furthermore, the temporal scheme requires only constant-coefficient Poisson and
Helmholtz linear solvers, enabling a very efficient and simple FFT-based
implementation on GPUs. We numerically investigate the performance of the
method on several standard test problems...Comment: Contains a number of corrections and an additional Figure 7 (and
associated discussion) relative to published versio
The Stokes-Einstein Relation at Moderate Schmidt Number
The Stokes-Einstein relation for the self-diffusion coefficient of a
spherical particle suspended in an incompressible fluid is an asymptotic result
in the limit of large Schmidt number, that is, when momentum diffuses much
faster than the particle. When the Schmidt number is moderate, which happens in
most particle methods for hydrodynamics, deviations from the Stokes-Einstein
prediction are expected. We study these corrections computationally using a
recently-developed minimally-resolved method for coupling particles to an
incompressible fluctuating fluid in both two and three dimensions. We find that
for moderate Schmidt numbers the diffusion coefficient is reduced relative to
the Stokes-Einstein prediction by an amount inversely proportional to the
Schmidt number in both two and three dimensions. We find, however, that the
Einstein formula is obeyed at all Schmidt numbers, consistent with linear
response theory. The numerical data is in good agreement with an approximate
self-consistent theory, which can be used to estimate finite-Schmidt number
corrections in a variety of methods. Our results indicate that the corrections
to the Stokes-Einstein formula come primarily from the fact that the particle
itself diffuses together with the momentum. Our study separates effects coming
from corrections to no-slip hydrodynamics from those of finite separation of
time scales, allowing for a better understanding of widely observed deviations
from the Stokes-Einstein prediction in particle methods such as molecular
dynamics.Comment: Submitte
Lattice Boltzmann based multicomponent reactive transport model coupled with geochemical solver for pore scale simulations
A Lattice Boltzmann (LB) based reactive transport model intended to capture
reactions and solid phase changes occurring at the pore scale is presented. The proposed
approach uses LB method to compute multi component mass transport. The LB multicomponent
transport model is then coupled with the well-established geochemical reaction
code PHREEQC which solves for thermodynamic equilibrium in mixed aqueous-solid phase
system with homogenous and heterogeneous reactions. This coupling enables us to update
solid phases volumes based on dissolution or precipitation using static update rules which, on
pore scale, affects the change of potentially pore network geometry. Unlike conventional
approach, heterogeneous reactions are conceptualized as volumetric reactions by introducing
additional source term in the fluid node next to solid node, and not as flux boundaries. To
demonstrate the validity of this approach several examples are presented in this paper
Simulating anomalous dispersion in porous media using the unstructured lattice Boltzmann method
Flow in porous media is a significant challenge to many computational fluid dynamics methods because of the complex boundaries separating pore fluid and host medium. However, the rapid development of the lattice Boltzmann methods and experimental imaging techniques now allow us to efficiently and robustly simulate flows in the pore space of porous rocks. Here we study the flow and dispersion in the pore space of limestone samples using the unstructured, characteristic based off-lattice Boltzmann method. We use the method to investigate the anomalous dispersion of particles in the pore space. We further show that the complex pore network limits the effectivity by which pollutants in the pore space can be removed by continuous flushing. In the smallest pores, diffusive transport dominates over advective transport and therefore cycles of flushing and no flushing, respectively, might be a more efficient strategy for pollutant removal
A random projection method for sharp phase boundaries in lattice Boltzmann simulations
Existing lattice Boltzmann models that have been designed to recover a macroscopic description of immiscible liquids are only able to make predictions that are quantitatively correct when the interface that exists between the fluids is smeared over several nodal points. Attempts to minimise the thickness of this interface generally leads to a phenomenon known as lattice pinning, the precise cause of which is not well understood. This spurious behaviour is remarkably similar to that associated with the numerical simulation of hyperbolic partial differential equations coupled with a stiff source term. Inspired by the seminal work in this field, we derive a lattice Boltzmann implementation of a model equation used to investigate such peculiarities. This implementation is extended to different spacial discretisations in one and two dimensions. We shown that the inclusion of a quasi-random threshold dramatically delays the onset of pinning and facetting
Evaluating the stability of numerical schemes for fluid solvers in game technology
A variety of numerical techniques have been explored to solve the shallow water equations in real-time water simulations for computer graphics applications. However, determining the stability of a numerical algorithm is a complex and involved task when a coupled set of nonlinear partial differential equations need to be solved. This paper proposes a novel and simple technique to compare the relative empirical stability of finite difference (or any grid-based scheme) algorithms by solving the inviscid Burgers’ equation to analyse their respective breaking times. To exemplify the method to evaluate numerical stability, a range of finite difference schemes is considered. The technique is effective at evaluating the relative stability of the considered schemes and demonstrates that the conservative schemes have superior stability
Simulation of two-phase flows at large density ratios and high Reynolds numbers using a discrete unified gas kinetic scheme
In order to treat immiscible two-phase flows at large density ratios and high
Reynolds numbers, a three-dimensional code based on the discrete unified gas
kinetic scheme (DUGKS) is developed, incorporating two major improvements.
First, the particle distribution functions at cell interfaces are reconstructed
using a weighted essentially non-oscillatory scheme. Second, the conservative
lower-order Allen-Cahn equation is chosen, instead of the higher-order
Cahn-Hilliard equation, to evolve the free-energy based phase field governing
the dynamics of two-phase interfaces. Five benchmark problems are simulated to
demonstrate the capability of the approach in treating two phase flows at large
density ratios and high Reynolds numbers, including three two dimensional
problems (a stationary droplet, Rayleigh-Taylor instability, and a droplet
splashing on a thin liquid film) and two three-dimensional problems (binary
droplets collision and Rayleigh-Taylor instability). All results agree well
with the previous numerical and the experimental results. In these simulations,
the density ratio and Reynolds number can reach a large value of O(1000). Our
improved approach sets the stage for the DUGKS scheme to handle realistic
two-phase flow problems
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