Well-Balanced Inundation Modeling for Shallow-Water Flows with Discontinuous Galerkin Schemes
Modeling coastal inundation for tsunami and storm surge hazard mitigation is an important application of geoscientific numerical modeling. While the complex topography demands for robust and locally accurate schemes, computational parallel efficiency and discrete conservation properties of the scheme are required. In order to meet these requirements, Runge-Kutta discontinuous Galerkin numerical methods are attractive. However, maintaining conservation and well-balancedness of these schemes with wetting/drying boundary conditions poses a challenge. We address this issue by a local nondestructive modification of the flux computation at boundary cells, which maintains accuracy, conservation and well-balancedness. The development can be viewed as a specialized flux limiter, which proves its usefulness with three different test cases for inundation simulation.
KeywordsDiscontinuous Galerkin Bottom Topography Shallow Water Equation Discontinuous Galerkin Method Discontinuous Galerkin Scheme
The authors would like to thank the Volkswagen foundation for their support through the ASCETE (Advanced Simulation of Coupled Earthquake and Tsunami Events) project. The second author also gratefully acknowledges support through ASTARTE—Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV.2013.6.4-3).
- 4.Beisiegel, N., Behrens, J., Castro, C.E.: Development of an adaptive discontinuous Galerkin inundation model. J. Comput. Phys. (Submitted) (2013)Google Scholar
- 7.Chen, C., Qi, J., Li, C., Beardsley, R.C., Lin, H., Walker, R., Gates, K.: Complexity of the flooding/drying process in an estuarine tidal-creek salt-marsh system: an application of FVCOM. J. Geophys. Res. 113, C07, 052 (2008). doi: 10.1029/2007jc004328
- 13.Kärnä, T., de Brye, B., Gourgue, O., Lambrechts, J., Comblen, R., Legat, V., Deleersnijder, E.: A fully implicit wetting-drying method for DG-FEM shallow water models, with an application to the scheldt estuary. Comput. Methods Appl. Mech. Eng. 200(5–8), 509–524 (2011). doi: 10.1016/j.cma.2010.07.001 CrossRefMATHGoogle Scholar
- 18.The Third International Workshop on Long-Wave Runup Models: Benchmark problem #1: Tsunami runup onto a plane beach (2004). http://isec.nacse.org/workshop/2004_cornell/bmark1.html