Abstract
We propose to couple our adaptive mesh refinement software PeanoClaw with existing solvers for complex overland flows that are tailored to regular Cartesian meshes. This allows us to augment them with spatial adaptivity and local time-stepping without altering the computational kernels. FullSWOF2D—Full Shallow Water Overland Flows—here is our software of choice though all paradigms hold for other solvers as well. We validate our hybrid simulation software in an artificial test scenario before we provide results for a large-scale flooding scenario of the Mecca region. The latter demonstrates that our coupling approach enables the simulation of complex “real-world” scenarios.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Acknowledgement
Audusse, E., Bouchut, F., Bristeau, M.-O., Klein, R., Perthame, B.: A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. 25(6), 2050–2065 (2013)
Berger, M.J., Colella, P.: Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82(1), 64–84 (1989)
Burstedde, C., Calhoun, D., Mandli, K., Terrel, A.R.: ForestClaw: hybrid forest-of-octrees AMR for hyperbolic conservation laws. In: Bader, M. Bode, A., Bungartz, H.-J., Gerndt, M., Joubert, G.R., Peters, F.J. (eds.) Parallel Computing: Accelerating Computational Science and Engineering (CSE), vol. 25. IOS Press, Amsterdam (2014)
Cordier, S., Coullon, H., Delestre, O., Laguerre, C., Le, M.-H., Pierre, D., Sadaka, G.: FullSWOF PARAL: comparison of two parallelization strategies (MPI and SkelGIS) on a software designed for hydrology application. In: Proceedings CEMRACS 2012, ESAIM: Proceedings, vol. 43, pp. 59–79 (2013)
Delestre, O., Lucas, C., Ksinant, P.-A., Darboux, F., Laguerre, C., Vo, T.N.T., James, F., Cordier, S.: SWASHES: a compilation of Shallow Water Analytic Solutions for Hydraulic and Environmental Studies, Int. J. Numer. Meth. Fl., 72(3), pp. 269–300 (2013)
Delestre, O., Cordier, S., Darboux, F., Mingxuan, D., James, F., Laguerre, C., Lucas, C., Planchon, O.: FullSWOF: a software for overland flow simulation. In: Gourbesville, P., Cunge, J., Caignaert, G. (eds.) Advances in Hydroinformatics – SIMHYDRO 2012 – New Frontiers of Simulation. Springer Hydrogeology, pp. 221–231. Springer, Singapore (2014)
Delestre, O., Darboux, F., James, F., Lucas, C., Laguerre, C., Cordier, S.: FullSWOF: a free software package for the simulation of shallow water flows. http://www.arxiv.org/abs/1401.4125 (2014)
Dumbser, M., Käser, M., Toro, E.F.: An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes – V. Local time stepping and p-adaptivity. Geophys. J. Int. 171(2), 695–717 (2007)
Dyck, S., Peschke, G.: Grundlagen der Hydrologie. Verlag für Bauwesen GmbH, Berlin (1995)
Green, W.H., Ampt, G.A.: Studies on soil physics: 1, flow of air and water through soils. J. Agric. Sci. 4, 1–24 (1911)
Ketcheson, D.I., Mandli, K., Ahmadia, A.J., Alghamdi, A., de Luna, M.Q., Parsani, M., Knepley, M.G., Emmett, M.: PyClaw: accessible, extensible, scalable tools for wave propagation problems. SIAM J. Sci. Comput. 34(4), C210–C231 (2012)
van Leer, B.: Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32, 101–139 (1979)
LeVeque, R.J., George, D.L., Berger, M.J.: Tsunami modelling with adaptively refined finite volume methods. Acta Numerica 20, 211–289 (2001)
Moussa, R., Bocquillon, C.: Approximation zones of the Saint-Venant equations for flood routing with overbank flow. Hydrol. Earth Syst. Sci. 4(2), 251–261 (2000)
Novak, P., Guinot, V., Jeffrey, A., Reeve, D.E.: Hydraulic Modelling – An Introduction. CRC Press, Boca Raton (2010)
Thabet, A., Smith, N., Wittmann, R., Schneider, J.: A visual framework for digital reconstruction of topographic maps. http://www.hdl.handle.net/10754/332722 (2014)
Unterweger K., Weinzierl, T., Ketcheson, D.I., Ahmadia, A.: Peanoclaw: a functionally-decomposed approach to adaptive mesh refinement with local time stepping for hyperbolic conservation law solvers. Technical Report TUM-I1332, Technische Universität München (2013)
Weinzierl, T., Mehl, M.: Peano – a traversal and storage scheme for octree-like adaptive cartesian multiscale grids. SIAM J. Sci. Comput. 33(5), 2732–2760 (2011)
Weinzierl, T., Others: Peano—a Framework for PDE solvers on spacetree grids. http://www.peano-framework.org (2012)
Weinzierl, T., Bader, M., Unterweger, K., Wittmann, R.: Block fusion on dynamically adaptive spacetree grids for shallow water waves. Parallel Process. Lett. 24(3), 1441006 (2014)
Acknowledgements
This work is partially supported by the Award No. UK-C0020 made by King Abdullah University of Science and Technology (KAUST). We also want to thank the KAUST Visual Computing Center for granting us access to the reconstructed data elevation maps of Mecca, Saudi-Arabia.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Unterweger, K., Wittmann, R., Neumann, P., Weinzierl, T., Bungartz, HJ. (2015). Integration of FULLSWOF2D and PeanoClaw: Adaptivity and Local Time-Stepping for Complex Overland Flows. In: Mehl, M., Bischoff, M., Schäfer, M. (eds) Recent Trends in Computational Engineering - CE2014. Lecture Notes in Computational Science and Engineering, vol 105. Springer, Cham. https://doi.org/10.1007/978-3-319-22997-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-22997-3_11
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22996-6
Online ISBN: 978-3-319-22997-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)