Abstract
The design of numerical boundary conditions in high order schemes is a challenging problem that has been tackled in different ways depending on the nature of the problem and the scheme used to solve it numerically. In this paper we propose a technique to extrapolate the information from the computational domain to ghost cells for schemes with structured Cartesian Meshes on complex domains. This technique is based on the application of Lagrange interpolation with weighted filters for the detection of discontinuities that permits a data dependent extrapolation, with high order at smooth regions and essentially non oscillatory properties near discontinuities. This paper is a sequel of Baeza et al. (J Sci Comput, 2015), where a boundary extrapolation procedure with Boolean filters was developed. We show that weighted extrapolation can tackle discontinuities more robustly than the procedure introduced in Baeza et al. (J Sci Comput, 2015).
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Acknowledgements
This research was partially supported by Spanish MINECO grants MTM2011-22741 and MTM2014-54388.
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Baeza, A., Mulet, P., Zorío, D. (2016). Weighted Extrapolation Techniques for Finite Difference Methods on Complex Domains with Cartesian Meshes. In: Ortegón Gallego, F., Redondo Neble, M., Rodríguez Galván, J. (eds) Trends in Differential Equations and Applications. SEMA SIMAI Springer Series, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-32013-7_14
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DOI: https://doi.org/10.1007/978-3-319-32013-7_14
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