411 research outputs found
Stable higher order finite-difference schemes for stellar pulsation calculations
Context: Calculating stellar pulsations requires a sufficient accuracy to
match the quality of the observations. Many current pulsation codes apply a
second order finite-difference scheme, combined with Richardson extrapolation
to reach fourth order accuracy on eigenfunctions. Although this is a simple and
robust approach, a number of drawbacks exist thus making fourth order schemes
desirable. A robust and simple finite-difference scheme, which can easily be
implemented in either 1D or 2D stellar pulsation codes is therefore required.
Aims: One of the difficulties in setting up higher order finite-difference
schemes for stellar pulsations is the so-called mesh-drift instability. Current
ways of dealing with this defect include introducing artificial viscosity or
applying a staggered grids approach. However these remedies are not well-suited
to eigenvalue problems, especially those involving non-dissipative systems,
because they unduly change the spectrum of the operator, introduce
supplementary free parameters, or lead to complications when applying boundary
conditions.
Methods: We propose here a new method, inspired from the staggered grids
strategy, which removes this instability while bypassing the above
difficulties. Furthermore, this approach lends itself to superconvergence, a
process in which the accuracy of the finite differences is boosted by one
order.
Results: This new approach is shown to be accurate, flexible with respect to
the underlying grid, and able to remove mesh-drift.Comment: 15 pages, 11 figures, accepted for publication in A&
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