678 research outputs found
Mixing effectiveness depends on the source-sink structure: Simulation results
The mixing effectiveness, i.e., the enhancement of molecular diffusion, of a
flow can be quantified in terms of the suppression of concentration variance of
a passive scalar sustained by steady sources and sinks. The mixing enhancement
defined this way is the ratio of the RMS fluctuations of the scalar mixed by
molecular diffusion alone to the (statistically steady-state) RMS fluctuations
of the scalar density in the presence of stirring. This measure of the
effectiveness of the stirring is naturally related to the enhancement factor of
the equivalent eddy diffusivity over molecular diffusion, and depends on the
Peclet number. It was recently noted that the maximum possible mixing
enhancement at a given Peclet number depends as well on the structure of the
sources and sinks. That is, the mixing efficiency, the effective diffusivity,
or the eddy diffusion of a flow generally depends on the sources and sinks of
whatever is being stirred. Here we present the results of particle-based
simulations quantitatively confirming the source-sink dependence of the mixing
enhancement as a function of Peclet number for a model flow.Comment: 13 pages, 9 figures, RevTex4 macro
Multiscale Modeling of Particle Transport in Petroleum Reservoirs
Modeling subsurface particle transport and retention is important for many processes, including sand production, fines migration, and nanoparticle injection. In this study, a pore-scale particle plugging simulator is concurrently coupled with a streamline reservoir simulator to predict the behavior of particles in the subsurface. The coupled simulators march forward in time together. The automated communication between the two models enables the prediction of spatially and time dependent parameters that control the particle transport process. At each time step, the reservoir simulator provides the inlet velocity and particle concentration of the fluid suspension to the pore-scale model which outputs the permeability, porosity, and retention coefficient. This permits the reservoir simulator to include pore-scale physics at selected locations to determine the number of particles retained and the formation damage. The pore-scale simulator tracks the path of individual particles as they are simultaneously injected into the sample and produces an effluent particle concentration curve that is fit with a continuum-scale advection-dispersion model. The advection-dispersion model is matched to the pore-scale data by adjusting two parameters: the dispersion and retention coefficient. The retention coefficient dictates the number of particles retained across a grid block in the reservoir simulator. Incorporating fundamental pore-scale physics into the streamline reservoir simulator improves its predictive ability by updating the particle retention and formation damage of a grid block at each time step
Hybrid approaches for multiple-species stochastic reaction-diffusion models
Reaction-diffusion models are used to describe systems in fields as diverse
as physics, chemistry, ecology and biology. The fundamental quantities in such
models are individual entities such as atoms and molecules, bacteria, cells or
animals, which move and/or react in a stochastic manner. If the number of
entities is large, accounting for each individual is inefficient, and often
partial differential equation (PDE) models are used in which the stochastic
behaviour of individuals is replaced by a description of the averaged, or mean
behaviour of the system. In some situations the number of individuals is large
in certain regions and small in others. In such cases, a stochastic model may
be inefficient in one region, and a PDE model inaccurate in another. To
overcome this problem, we develop a scheme which couples a stochastic
reaction-diffusion system in one part of the domain with its mean field
analogue, i.e. a discretised PDE model, in the other part of the domain. The
interface in between the two domains occupies exactly one lattice site and is
chosen such that the mean field description is still accurate there. This way
errors due to the flux between the domains are small. Our scheme can account
for multiple dynamic interfaces separating multiple stochastic and
deterministic domains, and the coupling between the domains conserves the total
number of particles. The method preserves stochastic features such as
extinction not observable in the mean field description, and is significantly
faster to simulate on a computer than the pure stochastic model.Comment: 38 pages, 8 figure
A non-hybrid method for the PDF equations of turbulent flows on unstructured grids
In probability density function (PDF) methods of turbulent flows, the joint
PDF of several flow variables is computed by numerically integrating a system
of stochastic differential equations for Lagrangian particles. A set of
parallel algorithms is proposed to provide an efficient solution of the PDF
transport equation, modeling the joint PDF of turbulent velocity, frequency and
concentration of a passive scalar in geometrically complex configurations. An
unstructured Eulerian grid is employed to extract Eulerian statistics, to solve
for quantities represented at fixed locations of the domain (e.g. the mean
pressure) and to track particles. All three aspects regarding the grid make use
of the finite element method (FEM) employing the simplest linear FEM shape
functions. To model the small-scale mixing of the transported scalar, the
interaction by exchange with the conditional mean model is adopted. An adaptive
algorithm that computes the velocity-conditioned scalar mean is proposed that
homogenizes the statistical error over the sample space with no assumption on
the shape of the underlying velocity PDF. Compared to other hybrid
particle-in-cell approaches for the PDF equations, the current methodology is
consistent without the need for consistency conditions. The algorithm is tested
by computing the dispersion of passive scalars released from concentrated
sources in two different turbulent flows: the fully developed turbulent channel
flow and a street canyon (or cavity) flow. Algorithmic details on estimating
conditional and unconditional statistics, particle tracking and particle-number
control are presented in detail. Relevant aspects of performance and
parallelism on cache-based shared memory machines are discussed.Comment: Accepted in Journal of Computational Physics, Feb. 20, 200
Multiscale stochastic reaction-diffusion modelling: application to actin dynamics in filopodia
Two multiscale (hybrid) stochastic reaction-diffusion models of actin dynamics in a filopodium are investigated. Both hybrid algorithms combine compartment-based and molecular-based stochastic reaction-diffusion models. The first hybrid model is based on the models previously\ud
developed in the literature. The second hybrid model is based on the application of recently developed two-regime method (TRM) to a fully molecular-based model which is also developed in this paper. The results of hybrid models are compared with the results of the molecular-based model. It is shown that both approaches give comparable results, although the TRM model better agrees quantitatively with the molecular-based model
Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics
Two algorithms that combine Brownian dynamics (BD) simulations with
mean-field partial differential equations (PDEs) are presented. This
PDE-assisted Brownian dynamics (PBD) methodology provides exact particle
tracking data in parts of the domain, whilst making use of a mean-field
reaction-diffusion PDE description elsewhere. The first PBD algorithm couples
BD simulations with PDEs by randomly creating new particles close to the
interface which partitions the domain and by reincorporating particles into the
continuum PDE-description when they cross the interface. The second PBD
algorithm introduces an overlap region, where both descriptions exist in
parallel. It is shown that to accurately compute variances using the PBD
simulation requires the overlap region. Advantages of both PBD approaches are
discussed and illustrative numerical examples are presented.Comment: submitted to SIAM Journal on Applied Mathematic
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