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Baines, M. J. (2015)
Publisher: Global Science Press
Languages: English
Types: Article
Subjects:
In order to move the nodes in a moving mesh method a time-stepping scheme is required which is ideally explicit and non-tangling (non-overtaking in one dimension (1-D)). Such a scheme is discussed in this paper, together with its drawbacks, and illustrated in 1-D in the context of a velocity-based Lagrangian conservation method applied to first order and second order examples which exhibit a regime change after node compression. An implementation in multidimensions is also described in some detail.
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    • [11] T.E.Lee, Modelling time dependent partial differential equations, PhD thesis, Department of Mathematics and Statistics, University of Reading, UK (2011).
    • [12] T.E.Lee, M.J.Baines and S.Langdon. A nite difference moving mesh method based on conservation for moving boundary problems. J. Comp and Applied Math, doi:10.1016/j.cam.2015.03.032 (2015).
    • [13] J. Vazquez, The Porous Medium Equation, OUP (2007).
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