540 research outputs found
A discontinuous Galerkin method for the Vlasov-Poisson system
A discontinuous Galerkin method for approximating the Vlasov-Poisson system
of equations describing the time evolution of a collisionless plasma is
proposed. The method is mass conservative and, in the case that piecewise
constant functions are used as a basis, the method preserves the positivity of
the electron distribution function and weakly enforces continuity of the
electric field through mesh interfaces and boundary conditions. The performance
of the method is investigated by computing several examples and error estimates
associated system's approximation are stated. In particular, computed results
are benchmarked against established theoretical results for linear advection
and the phenomenon of linear Landau damping for both the Maxwell and Lorentz
distributions. Moreover, two nonlinear problems are considered: nonlinear
Landau damping and a version of the two-stream instability are computed. For
the latter, fine scale details of the resulting long-time BGK-like state are
presented. Conservation laws are examined and various comparisons to theory are
made. The results obtained demonstrate that the discontinuous Galerkin method
is a viable option for integrating the Vlasov-Poisson system.Comment: To appear in Journal for Computational Physics, 2011. 63 pages, 86
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Direct Integration of the Collisionless Boltzmann Equation in Six-dimensional Phase Space: Self-gravitating Systems
We present a scheme for numerical simulations of collisionless
self-gravitating systems which directly integrates the Vlasov--Poisson
equations in six-dimensional phase space. By the results from a suite of
large-scale numerical simulations, we demonstrate that the present scheme can
simulate collisionless self-gravitating systems properly. The integration
scheme is based on the positive flux conservation method recently developed in
plasma physics. We test the accuracy of our code by performing several test
calculations including the stability of King spheres, the gravitational
instability and the Landau damping. We show that the mass and the energy are
accurately conserved for all the test cases we study. The results are in good
agreement with linear theory predictions and/or analytic solutions. The
distribution function keeps the property of positivity and remains
non-oscillatory. The largest simulations are run on 64^6 grids. The computation
speed scales well with the number of processors, and thus our code performs
efficiently on massively parallel supercomputers.Comment: 35 pages, 19 figures. Submitted to the Astrophysical Journa
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