Abstract
We review recent results in the development of a class of accurate, efficient, high order, dynamically p-adaptive Discontinuous Galerkin methods for geophysical flows. The proposed methods are able to capture phenomena at very different spatial scales, while minimizing the computational cost by means of a dynamical degree adaptation procedure and of a novel, fully second order, semi-implicit semi-Lagrangian time discretization. We then present novel results of the application of this technique to high resolution simulations of idealized non-hydrostatic flows.
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Acknowledgements
The authors would like to thank Filippo Giorgi for his continuous support and INDAM-GNCS for financial support in the framework of several projects and individual grants. Useful discussions with F.X. Giraldo on the topics addressed in this paper are also gratefully acknowledged.
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Tumolo, G., Bonaventura, L. (2020). Simulations of Non-hydrostatic Flows by an Efficient and Accurate p-Adaptive DG Method. In: van Brummelen, H., Corsini, A., Perotto, S., Rozza, G. (eds) Numerical Methods for Flows. Lecture Notes in Computational Science and Engineering, vol 132. Springer, Cham. https://doi.org/10.1007/978-3-030-30705-9_5
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DOI: https://doi.org/10.1007/978-3-030-30705-9_5
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