In:
Journal of Plasma Physics, Cambridge University Press (CUP), Vol. 88, No. 2 ( 2022-04)
Abstract:
First-order-accurate degenerate variational integration (DVI) was introduced in Ellison et al. ( Phys. Plasmas , vol. 25, 2018, 052502) for systems with a degenerate Lagrangian, i.e. one in which the velocity-space Hessian is singular. In this paper we introduce second-order-accurate DVI schemes, both with and without non-uniform time stepping. We show that it is not in general possible to construct a second-order scheme with a preserved two-form by composing a first-order scheme with its adjoint, and discuss the conditions under which such a composition is possible. We build two classes of second-order-accurate DVI schemes. We test these second-order schemes numerically on two systems having non-canonical variables, namely the magnetic field line and guiding centre systems. Variational integration for Hamiltonian systems with non-uniform time steps, in terms of an extended phase space Hamiltonian, is generalized to non-canonical variables. It is shown that preservation of proper degeneracy leads to single-step (one-step) methods without parasitic modes, i.e. to non-uniform time step DVIs. This extension applies to second-order-accurate as well as first-order schemes, and can be applied to adapt the time stepping to an error estimate.
Type of Medium:
Online Resource
ISSN:
0022-3778
,
1469-7807
DOI:
10.1017/S0022377821001136
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2022
detail.hit.zdb_id:
2004297-8
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