Article (Scientific journals)
Stable higher order finite-difference schemes for stellar pulsation calculations
Reese, Daniel
2013In Astronomy and Astrophysics, 555, p. 148
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Keywords :
methods: numerical; methods: analytical; stars: oscillations (including pulsations); stars: rotation
Abstract :
[en] 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 successfully applied to stellar pulsation calculations, and is shown to be accurate, flexible with respect to the underlying grid, and able to remove mesh-drift. Conclusions: Although specifically designed for stellar pulsation calculations, this method can easily be applied to many other physical or mathematical problems.
Disciplines :
Space science, astronomy & astrophysics
Author, co-author :
Reese, Daniel ;  Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Astrophysique stellaire théorique et astérosismologie
Language :
English
Title :
Stable higher order finite-difference schemes for stellar pulsation calculations
Publication date :
July 2013
Journal title :
Astronomy and Astrophysics
ISSN :
0004-6361
eISSN :
1432-0746
Publisher :
EDP Sciences, Les Ulis, France
Volume :
555
Pages :
A148
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
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