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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.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

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    • [2] M. J. Baines, M. E. Hubbard and P. K. Jimack. Velocity-based Moving Mesh Methods for Nonlinear Partial Differential Equations with Moving Boundaries. Commun. Comput. Phys., 10: 509-576, 2011.
    • [3] M. J. Baines and T. E. Lee. A large time step implicit moving mesh scheme for moving boundary problems. Numerical Methods for Partial Differential Equations, 30: 321-338, 2014.
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    • [8] W. Huang, Y. Ren and R. D. Russell. Moving Mesh Method Partial Differential Equations Based on the Equidistribution Principle. SIAM Journal of Numerical Analysis, 31: 709-730, 1994.
    • [9] W. Huang and R. D. Russell. Adaptive Moving Mesh Methods. Springer, 2011.
    • [10] W. L. Kath and D. S. Cohen. Waiting-time behaviour in a nonlinear diffusion equation. Stud. Appl. Math., 67: 79-106, 1982.
    • [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 finite difference moving mesh method based on conservation for moving boundary problems. J. Comput. Appl. Math., 288: 1-17, 2015.
    • [13] J. Vazquez. The Porous Medium Equation. Oxford University Press, 2007.
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