Non-hydrostatic mesoscale atmospheric modeling by the anisotropic mesh adaptive discontinuous Galerkin method (2401.10662v1)
Abstract: We deal with non-hydrostatic mesoscale atmospheric modeling using the fully implicit space-time discontinuous Galerkin method in combination with the anisotropic $hp$-mesh adaptation technique. The time discontinuous approximation allows the treatment of different meshes at different time levels in a natural way which can significantly reduce the number of degrees of freedom. The presented approach generates a sequence of triangular meshes consisting of possible anisotropic elements and varying polynomial approximation degrees such that the interpolation error is below the given tolerance and the number of degrees of freedom at each time step is minimal. We describe the discretization of the problem together with several implementation issues related to the treatment of boundary conditions, algebraic solver and adaptive choice of the size of the time steps.The computational performance of the proposed method is demonstrated on several benchmark problems.
- J. Comput. Phys. 373, 28–63 (2018)
- J. Comput. Phys. 231(19), 6323–6348 (2012)
- Comput. Fluids 198 (2020)
- Springer (2004)
- Charles University, Prague, Faculty of Mathematics and Physics (2000). https://msekce.karlin.mff.cuni.cz/~dolejsi/angen/
- Dolejší, V.: Semi-implicit interior penalty discontinuous Galerkin methods for viscous compressible flows. Commun. Comput. Phys. 4(2), 231–274 (2008)
- Charles University, Prague, Faculty of Mathematics and Physics (2020). https://msekce.karlin.mff.cuni.cz/~dolejsi/adgfem/
- Springer Series in Computational Mathematics 48. Springer, Cham (2015)
- Birkhäuser (2022)
- Comput. Fluids 117, 304–324 (2015)
- J. Sci. Comput. 95(2) (2023)
- Clarendon Press, Oxford (2003)
- Comput. Methods Appl. Mech. Engrg. 194, 5068–5082 (2005)
- J. Comput. Phys. 227(8), 3849–3877 (2008)
- SIAM J. Sci. Comput. 32(6), 3394–3425 (2010)
- J. Comput. Phys. 207(1), 129–150 (2005)
- Springer (2020)
- Mon. Weather Rev. 132(1), 133–153 (2004)
- Int. J. Numer. Methods Fluids 32(6), 725–744 (2000)
- Hunter, J.D.: Matplotlib: A 2D graphics environment. Computing in Science & Engineering 9(3), 90–95 (2007)
- J. Comput. Phys. 463 (2022)
- SIAM J. Sci. Comput. 26(1), 1–30 (2004)
- J. Comput. Phys. 489 (2023)
- J. Comput. Appl. Math. 427 (2023)
- J. Comput. Phys. 491 (2023)
- SIAM J. Sci. Comput. 31(3), 2231–2257 (2009)
- Robert, A.: Bubble convection experiments with a semi-implicit formulation of the Euler equations. J. Atmos. Sci. 50(13), 1865 – 1873 (1993)
- Mon. Weather Rev. 130, 2459–2480 (2002)
- Mon. Weather Rev. 122(11), 2623–2630 (1994)
- Meteorol. Atmos. Phys. pp. 287–301 (2003)
- Int. J. Numer. Meth. Fluids 17(1), 1– 22 (1993)
- J. Comput. Phys. 468 (2022)
- J. Comput. Phys. 268, 106 – 133 (2014)