2,208 research outputs found
Existence results for non-smooth second order differential inclusions, Convergence result for a numerical scheme and applications for modelling inelastic collisions
We are interested in existence results for second order differential
inclusions, involving finite number of unilateral constraints in an abstract
framework. These constraints are described by a set-valued operator, more
precisely a proximal normal cone to a time-dependent set. Moreover we extend a
numerical scheme, introduced in [8] and proved a convergence result. We propose
applications in modelling inelastic collisions between rigid particles too.Comment: 22 pages, 1 figur
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
The contact dynamics method for granular media
In this paper we review the simulation method of the non-smooth contact
dynamics. This technique was designed to solve the unilateral and frictional
contact problem for a large number of rigid bodies and has proved to be
especially valuable in research of dense granular materials during the last
decade. We present here the basic principles compared to other methods and the
detailed description of a 3D algorithm. We point out an artifact manifesting
itself in spurious sound waves and discuss the applicability of the method.Comment: for the proceedings of the 7th Granada Seminar, 23 pages, 8 figure
DynamO: A free O(N) general event-driven molecular-dynamics simulator
Molecular-dynamics algorithms for systems of particles interacting through
discrete or "hard" potentials are fundamentally different to the methods for
continuous or "soft" potential systems. Although many software packages have
been developed for continuous potential systems, software for discrete
potential systems based on event-driven algorithms are relatively scarce and
specialized. We present DynamO, a general event-driven simulation package which
displays the optimal O(N) asymptotic scaling of the computational cost with the
number of particles N, rather than the O(N log(N)) scaling found in most
standard algorithms. DynamO provides reference implementations of the best
available event-driven algorithms. These techniques allow the rapid simulation
of both complex and large (>10^6 particles) systems for long times. The
performance of the program is benchmarked for elastic hard sphere systems,
homogeneous cooling and sheared inelastic hard spheres, and equilibrium
Lennard-Jones fluids. This software and its documentation are distributed under
the GNU General Public license and can be freely downloaded from
http://marcusbannerman.co.uk/dynamo
Shocks in supersonic sand
We measure time-averaged velocity, density, and temperature fields for steady
granular flow past a wedge and calculate a speed of granular pressure
disturbances (sound speed) equal to 10% of the flow speed. The flow is
supersonic, forming shocks nearly identical to those in a supersonic gas.
Molecular dynamics simulations of Newton's laws and Monte Carlo simulations of
the Boltzmann equation yield fields in quantitative agreement with experiment.
A numerical solution of Navier-Stokes-like equations agrees with a molecular
dynamics simulation for experimental conditions excluding wall friction.Comment: 4 pages, 5 figure
An adaptive hierarchical domain decomposition method for parallel contact dynamics simulations of granular materials
A fully parallel version of the contact dynamics (CD) method is presented in
this paper. For large enough systems, 100% efficiency has been demonstrated for
up to 256 processors using a hierarchical domain decomposition with dynamic
load balancing. The iterative scheme to calculate the contact forces is left
domain-wise sequential, with data exchange after each iteration step, which
ensures its stability. The number of additional iterations required for
convergence by the partially parallel updates at the domain boundaries becomes
negligible with increasing number of particles, which allows for an effective
parallelization. Compared to the sequential implementation, we found no
influence of the parallelization on simulation results.Comment: 19 pages, 15 figures, published in Journal of Computational Physics
(2011
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