Abstract
In this work we present simulations of different types of geophysical problems using the Dune and Dune-Fem software framework. We consider two-phase flow in porous media, a Stokes-Darcy coupled problem, and atmospheric flow problems. The basis of our schemes is the Discontinuous Galerkin discretizations.
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Arnold, D.N., Brezzi, F., Cockburn, B., Marini, L.D.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39(5), 1749–1779 (2002)
Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Kornhuber, R., Ohlberger, M., Sander, O.: A generic grid interface for parallel and adaptive scientific computing. II: Implementation and tests in dune. Computing 82(2-3), 121–138 (2008)
Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Ohlberger, M., Sander, O.: A generic grid interface for parallel and adaptive scientific computing. I: Abstract framework. Computing 82(2-3), 103–119 (2008)
Bastian, P., Droske, M., Engwer, C., Klöfkorn, R., Neubauer, T., Rumpf, M.: Towards a unified framework for scientific computing. In: Kornhuber, R., Hoppe, R., Keyes, D., Périaux, J., Pironneau, O., Xu, J. (eds.) Proceedings of the 15th Conference on Domain Decomposition Methods. LNCSE, vol. 40, pp. 167–174. Springer, Heidelberg (1976)
Bastian, P., Rivière, B.: Superconvergence and H(div) projection for discontinuous Galerkin methods. Int. J. Numer. Methods Fluids 42(10), 1043–1057 (2003)
Bonaventura, L.: Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci. 35, 78–107 (1978)
Bryan, G.H., Fritsch, J.M.: A benchmark simulation for moist nonhydrostatic numerical models. Mon. Weath. Rev. 130, 2917–2928 (2002)
Chen, Z., Huan, G., Ma, Y.: Computational methods for multiphase flows in porous media. Computational Science & Engineering, vol. 2, xxix 531 p. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2006)
Ciarlet, P., Lions, J.: Handbook of numerical analysis. Finite element methods (Part 1), vol. II. North-Holland, Amsterdam (1991)
Cockburn, B., Kanschat, G., Schotzau, D., Schwab, C.: Local discontinuous Galerkin methods for the Stokes system. SIAM J. Numer. Anal. 40(1), 319–343 (2002)
Dedner, A.: Solving the system of Radiation Magnetohydrodynamics: for solar physical simulations in 3d. Ph.D. thesis, Universität Freiburg (2003), http://www.freidok.uni-freiburg.de/volltexte/1098/
Dedner, A., Klöfkorn, R.: A generic stabilization approach for higher order Discontinuous Galerkin methods for convection dominated problems. Preprint no. 8 (submitted to SIAM Sci. Comput.), Mathematisches Institut, Unversität Freiburg (2008), http://www.mathematik.uni-freiburg.de/IAM/homepages/robertk/postscript/dedner_kloefkorn_limiter.pdf
Dedner, A., Klöfkorn, R., Nolte, M., Ohlberger, M.: A generic interface for parallel and adaptive discretization schemes. Abstraction principles and the Dune-Fem module. Computing (to appear)
Doms, G., Förstner, J., Heise, E., Herzog, H.J., Raschendorfler, M., Schrodin, R., Reinhardt, T., Vogel, G.: A description of the nonhydrostatic regional model lm. part i: Physical parametrization. Internal Correspondence at the DWD, 1–126 (2005)
Epshteyn, Y., Rivière, B.: Fully implicit discontinuous finite element methods for two-phase flow. Appl. Numer. Math. 57(4), 383–401 (2007), doi:10.1016/j.apnum.2006.04.004
Ern, A., Mozolevski, I., Schuh, L.: Accurate velocity reconstruction for discontinuous Galerkin approximations of two-phase porous medium flows. C. R., Math., Acad. Sci. Paris 347(9-10), 551–554 (2009), doi:10.1016/j.crma.2009.02.011
Ern, A., Nicaise, S., Vohralík, M.: An accurate H(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. C. R., Math., Acad. Sci. Paris 345(12), 709–712 (2007), doi:10.1016/j.crma.2007.10.036
Helmig, R.: Multiphase flow and transport processes in the subsurface: a contribution to the modelling of hydrosystems. Springer, Berlin (1997)
Jäger, W., Mikelic, A., Neuss, N.: Asymptotic analysis of the laminar viscous flow over a porous bed. SIAM J. Sci. Comput. 22(6), 2006–2028 (2001)
Klein, R.: Asymptotics, structure, and integration of sound-proof atmospheric flow equations. Theo. Comp. Fluid Dyn. 23(3), 161–195 (2009)
Klöfkorn, R.: Numerics for Evolution Equations - A General Interface Based Design Concept. Ph.D. thesis, Universität Freiburg (2009), http://www.freidok.uni-freiburg.de/volltexte/7175/
Restelli, M., Giraldo, F.: A conservative discontinuous galerkin semi-implicit formulation for the navier-stokes equations in nonhydrostatic mesoscale modeling. J. Sci. Comput. 31, 2231–2257 (2009)
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Brdar, S., Dedner, A., Klöfkorn, R., Kränkel, M., Kröner, D. (2011). Simulation of Geophysical Problems with DUNE-FEM. In: Krause, E., Shokin, Y., Resch, M., Kröner, D., Shokina, N. (eds) Computational Science and High Performance Computing IV. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17770-5_8
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DOI: https://doi.org/10.1007/978-3-642-17770-5_8
Publisher Name: Springer, Berlin, Heidelberg
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