2,250 research outputs found
Kinetic Solvers with Adaptive Mesh in Phase Space
An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for
solving multi-dimensional kinetic equations by the discrete velocity method. A
Cartesian mesh for both configuration (r) and velocity (v) spaces is produced
using a tree of trees data structure. The mesh in r-space is automatically
generated around embedded boundaries and dynamically adapted to local solution
properties. The mesh in v-space is created on-the-fly for each cell in r-space.
Mappings between neighboring v-space trees implemented for the advection
operator in configuration space. We have developed new algorithms for solving
the full Boltzmann and linear Boltzmann equations with AMPS. Several recent
innovations were used to calculate the discrete Boltzmann collision integral
with dynamically adaptive mesh in velocity space: importance sampling,
multi-point projection method, and the variance reduction method. We have
developed an efficient algorithm for calculating the linear Boltzmann collision
integral for elastic and inelastic collisions in a Lorentz gas. New AMPS
technique has been demonstrated for simulations of hypersonic rarefied gas
flows, ion and electron kinetics in weakly ionized plasma, radiation and light
particle transport through thin films, and electron streaming in
semiconductors. We have shown that AMPS allows minimizing the number of cells
in phase space to reduce computational cost and memory usage for solving
challenging kinetic problems
Stabilized Lattice Boltzmann-Enskog method for compressible flows and its application to one and two-component fluids in nanochannels
A numerically stable method to solve the discretized Boltzmann-Enskog
equation describing the behavior of non ideal fluids under inhomogeneous
conditions is presented. The algorithm employed uses a Lagrangian
finite-difference scheme for the treatment of the convective term and a forcing
term to account for the molecular repulsion together with a
Bhatnagar-Gross-Krook relaxation term. In order to eliminate the spurious
currents induced by the numerical discretization procedure, we use a
trapezoidal rule for the time integration together with a version of the
two-distribution method of He et al. (J. Comp. Phys 152, 642 (1999)). Numerical
tests show that, in the case of one component fluid in the presence of a
spherical potential well, the proposed method reduces the numerical error by
several orders of magnitude. We conduct another test by considering the flow of
a two component fluid in a channel with a bottleneck and provide information
about the density and velocity field in this structured geometry.Comment: to appear in Physical Review
Complexity and simplicity of plasmas
This paper has two main parts. The first one presents a direct path from
microscopic dynamics to Debye screening, Landau damping and collisional
transport. It shows there is more simplicity in microscopic plasma physics than
previously thought. The second part is more subjective. It describes some
difficulties in facing plasma complexity in general, suggests an inquiry about
the methods used empirically to tackle complex systems, discusses the teaching
of plasma physics as a physics of complexity, and proposes new directions to
face the inflation of information.Comment: 13 page
On collisional capture rates of irregular satellites around the gas-giant planets and the minimum mass of the solar nebula
We investigated the probability that an inelastic collision of planetesimals
within the Hill sphere of the Jovian planets could explain the presence and
orbits of observed irregular satellites. Capture of satellites via this
mechanism is highly dependent on not only the mass of the protoplanetary disk,
but also the shape of the planetesimal size distribution. We performed 2000
simulations for integrated time intervals Myr and found that, given
the currently accepted value for the minimum mass solar nebula and planetesimal
number density based upon the \citet{Nesvorny2003} and \citet{Charnoz2003} size
distribution , the collision rates for the different
Jovian planets range between and \gtrsim 170 \, \Myr^{-1} for
objects with radii, 1 \, \km \le r \le 10 \, \km. Additionally, we found that
the probability that these collisions remove enough orbital energy to yield a
bound orbit was and had very little dependence on the
relative size of the planetesimals. Of these collisions, the collision energy
between two objects was times the gravitational binding energy
for objects with radii km. We find that, capturing irregular
satellites via collisions between unbound objects can only account for of the observed population, hence can this not be the sole method of
producing irregular satellites.Comment: 11 pages 4 figures 1 table; This replaces a prior submission, which
contained some minor contradictions within the text accepted by MNRAS in
pres
Lattice Boltzmann simulations of soft matter systems
This article concerns numerical simulations of the dynamics of particles
immersed in a continuum solvent. As prototypical systems, we consider colloidal
dispersions of spherical particles and solutions of uncharged polymers. After a
brief explanation of the concept of hydrodynamic interactions, we give a
general overview over the various simulation methods that have been developed
to cope with the resulting computational problems. We then focus on the
approach we have developed, which couples a system of particles to a lattice
Boltzmann model representing the solvent degrees of freedom. The standard D3Q19
lattice Boltzmann model is derived and explained in depth, followed by a
detailed discussion of complementary methods for the coupling of solvent and
solute. Colloidal dispersions are best described in terms of extended particles
with appropriate boundary conditions at the surfaces, while particles with
internal degrees of freedom are easier to simulate as an arrangement of mass
points with frictional coupling to the solvent. In both cases, particular care
has been taken to simulate thermal fluctuations in a consistent way. The
usefulness of this methodology is illustrated by studies from our own research,
where the dynamics of colloidal and polymeric systems has been investigated in
both equilibrium and nonequilibrium situations.Comment: Review article, submitted to Advances in Polymer Science. 16 figures,
76 page
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