219 research outputs found
Lattice Boltzmann Magnetohydrodynamics
Lattice gas and lattice Boltzmann methods are recently developed numerical
schemes for simulating a variety of physical systems. In this paper a new
lattice Boltzmann model for modeling two-dimensional incompressible
magnetohydrodynamics (MHD) is presented. The current model fully utilizes the
flexibility of the lattice Boltzmann method in comparison with previous lattice
gas and lattice Boltzmann
MHD models, reducing the number of moving directions from in other
models to only. To increase computational efficiency, a simple single time
relaxation rule is used for collisions, which directly controls the transport
coefficients.
The bi-directional streaming process of the particle distribution function in
this paper is similar to the original model [ H. Chen and W. H. Matthaeus,
Phys. Rev. Lett., {\bf 58}, 1845(1987), S.Chen, H.Chen, D.Mart\'{\i}nez and
W.H.Matthaeus, Phys. Rev. Lett. {\bf 67},3776 (1991)], but has been greatly
simplified, affording simpler implementation of boundary conditions and
increasing the feasibility of extension into a workable three-dimensional
model. Analytical expressions for the transport coefficients are presented.
Also, as example cases, numerical calculation for the Hartmann flow is
performed, showing a good agreement between the theoreticalComment: 45 pages, to appear in Physics of Plasma
Steady State Convergence Acceleration of the Generalized Lattice Boltzmann Equation with Forcing Term through Preconditioning
Several applications exist in which lattice Boltzmann methods (LBM) are used
to compute stationary states of fluid motions, particularly those driven or
modulated by external forces. Standard LBM, being explicit time-marching in
nature, requires a long time to attain steady state convergence, particularly
at low Mach numbers due to the disparity in characteristic speeds of
propagation of different quantities. In this paper, we present a preconditioned
generalized lattice Boltzmann equation (GLBE) with forcing term to accelerate
steady state convergence to flows driven by external forces. The use of
multiple relaxation times in the GLBE allows enhancement of the numerical
stability. Particular focus is given in preconditioning external forces, which
can be spatially and temporally dependent. In particular, correct forms of
moment-projections of source/forcing terms are derived such that they recover
preconditioned Navier-Stokes equations with non-uniform external forces. As an
illustration, we solve an extended system with a preconditioned lattice kinetic
equation for magnetic induction field at low magnetic Prandtl numbers, which
imposes Lorentz forces on the flow of conducting fluids. Computational studies,
particularly in three-dimensions, for canonical problems show that the number
of time steps needed to reach steady state is reduced by orders of magnitude
with preconditioning. In addition, the preconditioning approach resulted in
significantly improved stability characteristics when compared with the
corresponding single relaxation time formulation.Comment: 47 pages, 21 figures, for publication in Journal of Computational
Physic
25 Years of Self-Organized Criticality: Solar and Astrophysics
Shortly after the seminal paper {\sl "Self-Organized Criticality: An
explanation of 1/f noise"} by Bak, Tang, and Wiesenfeld (1987), the idea has
been applied to solar physics, in {\sl "Avalanches and the Distribution of
Solar Flares"} by Lu and Hamilton (1991). In the following years, an inspiring
cross-fertilization from complexity theory to solar and astrophysics took
place, where the SOC concept was initially applied to solar flares, stellar
flares, and magnetospheric substorms, and later extended to the radiation belt,
the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar
glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and
boson clouds. The application of SOC concepts has been performed by numerical
cellular automaton simulations, by analytical calculations of statistical
(powerlaw-like) distributions based on physical scaling laws, and by
observational tests of theoretically predicted size distributions and waiting
time distributions. Attempts have been undertaken to import physical models
into the numerical SOC toy models, such as the discretization of
magneto-hydrodynamics (MHD) processes. The novel applications stimulated also
vigorous debates about the discrimination between SOC models, SOC-like, and
non-SOC processes, such as phase transitions, turbulence, random-walk
diffusion, percolation, branching processes, network theory, chaos theory,
fractality, multi-scale, and other complexity phenomena. We review SOC studies
from the last 25 years and highlight new trends, open questions, and future
challenges, as discussed during two recent ISSI workshops on this theme.Comment: 139 pages, 28 figures, Review based on ISSI workshops "Self-Organized
Criticality and Turbulence" (2012, 2013, Bern, Switzerland
Recent Advances in Understanding Particle Acceleration Processes in Solar Flares
We review basic theoretical concepts in particle acceleration, with
particular emphasis on processes likely to occur in regions of magnetic
reconnection. Several new developments are discussed, including detailed
studies of reconnection in three-dimensional magnetic field configurations
(e.g., current sheets, collapsing traps, separatrix regions) and stochastic
acceleration in a turbulent environment. Fluid, test-particle, and
particle-in-cell approaches are used and results compared. While these studies
show considerable promise in accounting for the various observational
manifestations of solar flares, they are limited by a number of factors, mostly
relating to available computational power. Not the least of these issues is the
need to explicitly incorporate the electrodynamic feedback of the accelerated
particles themselves on the environment in which they are accelerated. A brief
prognosis for future advancement is offered.Comment: This is a chapter in a monograph on the physics of solar flares,
inspired by RHESSI observations. The individual articles are to appear in
Space Science Reviews (2011
Multiscale modelling of the influence of convection on dendrite formation and freckle initiation during vacuum arc remelting
Vacuum Arc Remelting (VAR) is employed to produce homogeneous ingots with a
controlled, fine, microstructure. It is applied to reactive and segregation prone alloys
where convection can influence microstructure and defect formation. In this study, a
microscopic solidification model was extended to incorporate both forced and natural
convection. The Navier-Stokes equations were solved for liquid and mushy zones using a
modified projection method. The energy conservation and solute diffusion equations
were solved via a combined stochastic nucleation approach along with a finite difference
solution to simulate dendritic growth. This microscopic model was coupled to a 3D
transient VAR model which was developed by using a multi-physics modelling software
package, PHYSICA. The multiscale model enables simulations covering the range from
dendrites (in microns) to the complete process (in meters). These numerical models were
used to investigate: (i) the formation of dendritic microstructures under natural and forced
convections; (ii) initiation of solute channels (freckles) in directional solidification in
terms of interdendritic thermosolutal convection; and (iii) the macroscopic physical
dynamics in VAR and their influence on freckle formation.
2D and 3D dendritic microstructure were simulated by taking into account both solutal
and thermal diffusion for both constrained and unconstrained growth using the
solidification model. For unconstrained equiaxed dendritic growth, forced convection
was found to enhance dendritic growth in the upstream region while retarding
downstream growth. In terms of dimensionality, dendritic growth in 3D is faster than 2D
and convection promotes the coarsening of perpendicular arms and side branching in 3D.
For constrained columnar dendritic growth, downward interdendritic convection is
stopped by primary dendritic arms in 2D; this was not the case in 3D. Consequently, 3D
simulations must be used when studying thermosolutal convection during solidification,
since 2D simulations lead to inappropriate results. The microscopic model was also used
to study the initiation of freckles for Pb-Sn alloys, predicting solute channel formation
during directional solidification at a microstructural level for the first time. These
simulations show that the local remelting due to high solute concentrations and
continuous upward convection of segregated liquid result in the formation of sustained
open solute channels. High initial Sn compositions, low casting speeds and low
temperature gradients, all promote the initiation of these solute channels and hence
freckles.
to study the initiation of freckles for Pb-Sn alloys, predicting solute channel formation
during directional solidification at a microstructural level for the first time. These
simulations show that the local remelting due to high solute concentrations and
continuous upward convection of segregated liquid result in the formation of sustained
open solute channels. High initial Sn compositions, low casting speeds and low
temperature gradients, all promote the initiation of these solute channels and hence
freckles
Magnetohydrodynamic turbulence: The development of lattice Boltzmann methods for dissipative systems
Computer simulations of complex phenomena have become an invaluable tool for scientists in all disciplines. These simulations serve as a tool both for theorists attempting to test the validity of new theories and for experimentalists wishing to obtain a framework for the design of new experiments. Lattice Boltzmann Methods (LBM) provide a kinetic simulation technique for solving systems governed by non-linear conservation equations. Direct LBMs use the linearized single time relaxation form of the Boltzmann equation to temporally evolve particle distribution functions on a discrete spatial lattice. We will begin with a development of LBMs from basic kinetic theory and will then show how one can construct LBMs to model incompressible resistive magnetohydrodynamic (MHD) conservation laws. We will then present our work in extending existing models to the octagonal lattice, showing that the increased isotropy of the octagonal lattice produces better numerical stability and higher Reynolds numbers in MHD simulations. Finally, we will develop LBMs that use non-uniform grids and apply them to one dimensional MHD systems
AFCI Quarterly Input – UNLV July 1 through September 30, 2006
Quarterly report highlighting research projects, activities and objectives of the Transmutation Research Program at the Nuclear Science & Technology Division, Harry Reid Research Center.
The University of Nevada, Las Vegas supports the AFCI through research and development of technologies for economic and environmentally sound refinement of spent nuclear fuel. The UNLV program has four components: infrastructure, international collaboration, student-based research, and management and program support
Methods for stabilizing high Reynolds number Lattice Boltzmann simulations
The Lattice Boltzmann Method (LBM) is a simple and highly efficient method for computing nearly incompressible fluid flow. However, it is well known to suffer from numerical instabilities for low values of the transport coefficients. This dissertation examines a number of methods for increasing the stability of the LBM over a wide range of parameters. First, we consider a simple transformation that renders the standard LB equation implicit. It is found that the stability is largely unchanged. Next, we consider a stabilization method based on introducing a Lyapunov function which is essentially a discrete-time H-function. The uniqueness of an H-function that appears in the literature is proven, and the method is extended to stabilize some of the more popular LB models. We also introduce a new method for implementing boundary conditions in the LBM. The hydrodynamic fields are imposed in a transformed moment space, whereas The non-hydrodynamic fields are shifted over from neighboring nodes. By minimizing population gradients, this method exhibits superior numerical stability over other widely employed schemes when tested on the widely-used benchmark of incompressible flow over a backwards-facing step
AFCI Quarterly Input – UNLV January 1 through March 31, 2007
Quarterly report highlighting research projects, activities and objectives of the Transmutation Research Program at the Nuclear Science & Technology Division, Harry Reid Research Center.
The University of Nevada, Las Vegas supports the AFCI through research and development of technologies for economic and environmentally sound refinement of spent nuclear fuel. The UNLV program has four components: infrastructure, international collaboration, student-based research, and management and program support
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