38,209 research outputs found
An Arbitrary Curvilinear Coordinate Method for Particle-In-Cell Modeling
A new approach to the kinetic simulation of plasmas in complex geometries,
based on the Particle-in- Cell (PIC) simulation method, is explored. In the two
dimensional (2d) electrostatic version of our method, called the Arbitrary
Curvilinear Coordinate PIC (ACC-PIC) method, all essential PIC operations are
carried out in 2d on a uniform grid on the unit square logical domain, and
mapped to a nonuniform boundary-fitted grid on the physical domain. As the
resulting logical grid equations of motion are not separable, we have developed
an extension of the semi-implicit Modified Leapfrog (ML) integration technique
to preserve the symplectic nature of the logical grid particle mover. A
generalized, curvilinear coordinate formulation of Poisson's equations to solve
for the electrostatic fields on the uniform logical grid is also developed. By
our formulation, we compute the plasma charge density on the logical grid based
on the particles' positions on the logical domain. That is, the plasma
particles are weighted to the uniform logical grid and the self-consistent mean
electrostatic fields obtained from the solution of the logical grid Poisson
equation are interpolated to the particle positions on the logical grid. This
process eliminates the complexity associated with the weighting and
interpolation processes on the nonuniform physical grid and allows us to run
the PIC method on arbitrary boundary-fitted meshes.Comment: Submitted to Computational Science & Discovery December 201
SHARP: A Spatially Higher-order, Relativistic Particle-in-Cell Code
Numerical heating in particle-in-cell (PIC) codes currently precludes the
accurate simulation of cold, relativistic plasma over long periods, severely
limiting their applications in astrophysical environments. We present a
spatially higher-order accurate relativistic PIC algorithm in one spatial
dimension, which conserves charge and momentum exactly. We utilize the
smoothness implied by the usage of higher-order interpolation functions to
achieve a spatially higher-order accurate algorithm (up to fifth order). We
validate our algorithm against several test problems -- thermal stability of
stationary plasma, stability of linear plasma waves, and two-stream instability
in the relativistic and non-relativistic regimes. Comparing our simulations to
exact solutions of the dispersion relations, we demonstrate that SHARP can
quantitatively reproduce important kinetic features of the linear regime. Our
simulations have a superior ability to control energy non-conservation and
avoid numerical heating in comparison to common second-order schemes. We
provide a natural definition for convergence of a general PIC algorithm: the
complement of physical modes captured by the simulation, i.e., those that lie
above the Poisson noise, must grow commensurately with the resolution. This
implies that it is necessary to simultaneously increase the number of particles
per cell and decrease the cell size. We demonstrate that traditional ways for
testing for convergence fail, leading to plateauing of the energy error. This
new PIC code enables us to faithfully study the long-term evolution of plasma
problems that require absolute control of the energy and momentum conservation.Comment: 26 pages, 19 figures, discussion about performance is added,
published in Ap
Adaptive meshless refinement schemes for RBF-PUM collocation
In this paper we present an adaptive discretization technique for solving
elliptic partial differential equations via a collocation radial basis function
partition of unity method. In particular, we propose a new adaptive scheme
based on the construction of an error indicator and a refinement algorithm,
which used together turn out to be ad-hoc strategies within this framework. The
performance of the adaptive meshless refinement scheme is assessed by numerical
tests
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