142,722 research outputs found
Structure-Preserving Discretization of Incompressible Fluids
The geometric nature of Euler fluids has been clearly identified and
extensively studied over the years, culminating with Lagrangian and Hamiltonian
descriptions of fluid dynamics where the configuration space is defined as the
volume-preserving diffeomorphisms, and Kelvin's circulation theorem is viewed
as a consequence of Noether's theorem associated with the particle relabeling
symmetry of fluid mechanics. However computational approaches to fluid
mechanics have been largely derived from a numerical-analytic point of view,
and are rarely designed with structure preservation in mind, and often suffer
from spurious numerical artifacts such as energy and circulation drift. In
contrast, this paper geometrically derives discrete equations of motion for
fluid dynamics from first principles in a purely Eulerian form. Our approach
approximates the group of volume-preserving diffeomorphisms using a finite
dimensional Lie group, and associated discrete Euler equations are derived from
a variational principle with non-holonomic constraints. The resulting discrete
equations of motion yield a structure-preserving time integrator with good
long-term energy behavior and for which an exact discrete Kelvin's circulation
theorem holds
The computational complexity of traditional Lattice-Boltzmann methods for incompressible fluids
It is well-known that in fluid dynamics an alternative to customary direct
solution methods (based on the discretization of the fluid fields) is provided
by so-called \emph{particle simulation methods}. Particle simulation methods
rely typically on appropriate \emph{kinetic models} for the fluid equations
which permit the evaluation of the fluid fields in terms of suitable
expectation values (or \emph{momenta}) of the kinetic distribution function
being respectively and\textbf{\}
the position an velocity of a test particle with probability density
. These kinetic models can be continuous or discrete in
phase space, yielding respectively \emph{continuous} or \emph{discrete kinetic
models} for the fluids. However, also particle simulation methods may be biased
by an undesirable computational complexity. In particular, a fundamental issue
is to estimate the algorithmic complexity of numerical simulations based on
traditional LBM's (Lattice-Boltzmann methods; for review see Succi, 2001
\cite{Succi}). These methods, based on a discrete kinetic approach, represent
currently an interesting alternative to direct solution methods. Here we intend
to prove that for incompressible fluids fluids LBM's may present a high
complexity. The goal of the investigation is to present a detailed account of
the origin of the various complexity sources appearing in customary LBM's. The
result is relevant to establish possible strategies for improving the numerical
efficiency of existing numerical methods.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008
Lattice Boltzmann Thermohydrodynamics
We introduce a lattice Boltzmann computational scheme capable of modeling
thermohydrodynamic flows of monatomic gases. The parallel nature of this
approach provides a numerically efficient alternative to traditional methods of
computational fluid dynamics. The scheme uses a small number of discrete
velocity states and a linear, single-time-relaxation collision operator.
Numerical simulations in two dimensions agree well with exact solutions for
adiabatic sound propagation and Couette flow with heat transfer.Comment: 11 pages, Physical Review E: Rapid Communications, in pres
A Coupling Algorithm of Computational Fluid and Particle Dynamics (CFPD)
Computational fluid dynamics (CFD) and particle hydrodynamics (PHD) have been developed almost independently. CFD is classified into Eulerian and Lagrangian. The Eulerian approach observes fluid motion at specific locations in the space, and the Lagrangian approach looks at fluid motion where the observer follows an individual fluid parcel moving through space and time. In classical mechanics, particle dynamic simulations include molecular dynamics, Brownian dynamics, dissipated particle dynamics, Stokesian dynamics, and granular dynamics (often called discrete element method). Dissipative hydrodynamic method unifies these dynamic simulation algorithms and provides a general view of how to mimic particle motion in gas and liquid. Studies on an accurate and rigorous coupling of CFD and PHD are in literature still in a growing stage. This chapter shortly reviews the past development of CFD and PHD and proposes a general algorithm to couple the two dynamic simulations without losing theoretical rigor and numerical accuracy of the coupled simulation
Inpainting Computational Fluid Dynamics with Deep Learning
Fluid data completion is a research problem with high potential benefit for
both experimental and computational fluid dynamics. An effective fluid data
completion method reduces the required number of sensors in a fluid dynamics
experiment, and allows a coarser and more adaptive mesh for a Computational
Fluid Dynamics (CFD) simulation. However, the ill-posed nature of the fluid
data completion problem makes it prohibitively difficult to obtain a
theoretical solution and presents high numerical uncertainty and instability
for a data-driven approach (e.g., a neural network model). To address these
challenges, we leverage recent advancements in computer vision, employing the
vector quantization technique to map both complete and incomplete fluid data
spaces onto discrete-valued lower-dimensional representations via a two-stage
learning procedure. We demonstrated the effectiveness of our approach on
Kolmogorov flow data (Reynolds number: 1000) occluded by masks of different
size and arrangement. Experimental results show that our proposed model
consistently outperforms benchmark models under different occlusion settings in
terms of point-wise reconstruction accuracy as well as turbulent energy
spectrum and vorticity distribution.Comment: 20 pages, 9 figure
Continuous and discrete Clebsch variational principles
The Clebsch method provides a unifying approach for deriving variational
principles for continuous and discrete dynamical systems where elements of a
vector space are used to control dynamics on the cotangent bundle of a Lie
group \emph{via} a velocity map. This paper proves a reduction theorem which
states that the canonical variables on the Lie group can be eliminated, if and
only if the velocity map is a Lie algebra action, thereby producing the
Euler-Poincar\'e (EP) equation for the vector space variables. In this case,
the map from the canonical variables on the Lie group to the vector space is
the standard momentum map defined using the diamond operator. We apply the
Clebsch method in examples of the rotating rigid body and the incompressible
Euler equations. Along the way, we explain how singular solutions of the EP
equation for the diffeomorphism group (EPDiff) arise as momentum maps in the
Clebsch approach. In the case of finite dimensional Lie groups, the Clebsch
variational principle is discretised to produce a variational integrator for
the dynamical system. We obtain a discrete map from which the variables on the
cotangent bundle of a Lie group may be eliminated to produce a discrete EP
equation for elements of the vector space. We give an integrator for the
rotating rigid body as an example. We also briefly discuss how to discretise
infinite-dimensional Clebsch systems, so as to produce conservative numerical
methods for fluid dynamics
Modeling particle-fluid interaction in a coupled CFD-DEM framework
In this work, we present an alternative methodology to solve the
particle-fluid interaction in the resolved CFDEM coupling framework. This
numerical approach consists of coupling a Discrete Element Method (DEM) with a
Computational Fluid Dynamics (CFD) scheme, solving the motion of immersed
particles in a fluid phase. As a novelty, our approach explicitly accounts for
the body force acting on the fluid phase when computing the local momentum
balance equations. Accordingly, we implement a fluid-particle interaction
computing the buoyant and drag forces as a function of local shear strain and
pressure gradient. As a benchmark, we study the Stokesian limit of a single
particle. The validation is performed comparing our outcomes with the ones
provided by a previous resolved methodology and the analytical prediction. In
general, we find that the new implementation reproduces with very good accuracy
the Stokesian dynamics. Complementarily, we study the settling terminal
velocity of a sphere under confined conditions
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