127 research outputs found
High order and energy preserving discontinuous Galerkin methods for the Vlasov-Poisson system
We present a computational study for a family of discontinuous Galerkin
methods for the one dimensional Vlasov-Poisson system that has been recently
introduced. We introduce a slight modification of the methods to allow for
feasible computations while preserving the properties of the original methods.
We study numerically the verification of the theoretical and convergence
analysis, discussing also the conservation properties of the schemes. The
methods are validated through their application to some of the benchmarks in
the simulation of plasma physics.Comment: 44 pages, 28 figure
High Order Maximum Principle Preserving Semi-Lagrangian Finite Difference WENO schemes for the Vlasov Equation
In this paper, we propose the parametrized maximum principle preserving (MPP)
flux limiter, originally developed in [Z. Xu, Math. Comp., (2013), in press],
to the semi- Lagrangian finite difference weighted essentially non-oscillatory
scheme for solving the Vlasov equation. The MPP flux limiter is proved to
maintain up to fourth order accuracy for the semi-Lagrangian finite difference
scheme without any time step restriction. Numerical studies on the
Vlasov-Poisson system demonstrate the performance of the proposed method and
its ability in preserving the positivity of the probability distribution
function while maintaining the high order accuracy
Energy-conserving discontinuous Galerkin methods for the Vlasov-Amp\`{e}re system
In this paper, we propose energy-conserving numerical schemes for the
Vlasov-Amp\`{e}re (VA) systems. The VA system is a model used to describe the
evolution of probability density function of charged particles under self
consistent electric field in plasmas. It conserves many physical quantities,
including the total energy which is comprised of the kinetic and electric
energy. Unlike the total particle number conservation, the total energy
conservation is challenging to achieve. For simulations in longer time ranges,
negligence of this fact could cause unphysical results, such as plasma self
heating or cooling. In this paper, we develop the first Eulerian solvers that
can preserve fully discrete total energy conservation. The main components of
our solvers include explicit or implicit energy-conserving temporal
discretizations, an energy-conserving operator splitting for the VA equation
and discontinuous Galerkin finite element methods for the spatial
discretizations. We validate our schemes by rigorous derivations and benchmark
numerical examples such as Landau damping, two-stream instability and
bump-on-tail instability
Conservative and non-conservative methods based on hermite weighted essentially-non-oscillatory reconstruction for Vlasov equations
We introduce a WENO reconstruction based on Hermite interpolation both for
semi-Lagrangian and finite difference methods. This WENO reconstruction
technique allows to control spurious oscillations. We develop third and fifth
order methods and apply them to non-conservative semi-Lagrangian schemes and
conservative finite difference methods. Our numerical results will be compared
to the usual semi-Lagrangian method with cubic spline reconstruction and the
classical fifth order WENO finite difference scheme. These reconstructions are
observed to be less dissipative than the usual weighted essentially non-
oscillatory procedure. We apply these methods to transport equations in the
context of plasma physics and the numerical simulation of turbulence phenomena
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