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Mixed semi-Lagrangian/finite difference methods for plasma simulations
In this paper, we present an efficient algorithm for the long time behavior
of plasma simulations. We will focus on 4D drift-kinetic model, where the
plasma's motion occurs in the plane perpendicular to the magnetic field and can
be governed by the 2D guiding-center model.
Hermite WENO reconstructions, already proposed in \cite{YF15}, are applied
for solving the Vlasov equation. Here we consider an arbitrary computational
domain with an appropriate numerical method for the treatment of boundary
conditions.
Then we apply this algorithm for plasma turbulence simulations. We first
solve the 2D guiding-center model in a D-shape domain and investigate the
numerical stability of the steady state. Then, the 4D drift-kinetic model is
studied with a mixed method, i.e. the semi-Lagrangian method in linear phase
and finite difference method during the nonlinear phase. Numerical results show
that the mixed method is efficient and accurate in linear phase and it is much
stable during the nonlinear phase. Moreover, in practice it has better
conservation properties.Comment: arXiv admin note: text overlap with arXiv:1312.448
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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