Vater, S. and Beisiegel, N. and Behrens, J.
(2019)
*A limiter‐based well‐balanced discontinuous Galerkin method for shallow‐water flows with wetting and drying: Triangular grids.*
International Journal for Numerical Methods in Fluids, 91
(8).
pp. 395-418.

Full text not available from this repository.

Official URL: https://doi.org/10.1002/fld.4762

## Abstract

A novel wetting and drying treatment for second‐order Runge‐Kutta discontinuous Galerkin methods solving the nonlinear shallow‐water equations is proposed. It is developed for general conforming two‐dimensional triangular meshes and utilizes a slope limiting strategy to accurately model inundation. The method features a nondestructive limiter, which concurrently meets the requirements for linear stability and wetting and drying. It further combines existing approaches for positivity preservation and well balancing with an innovative velocity‐based limiting of the momentum. This limiting controls spurious velocities in the vicinity of the wet/dry interface. It leads to a computationally stable and robust scheme, even on unstructured grids, and allows for large time steps in combination with explicit time integrators. The scheme comprises only one free parameter, to which it is not sensitive in terms of stability. A number of numerical test cases, ranging from analytical tests to near‐realistic laboratory benchmarks, demonstrate the performance of the method for inundation applications. In particular, superlinear convergence, mass conservation, well balancedness, and stability are verified.

Item Type: | Article |
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Additional Information: | open access article |

Uncontrolled Keywords: | discontinuous Galerkin methods limiter hallow-water equations stability well-balanced schemes wetting and drying |

Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group |

ID Code: | 2397 |

Deposited By: | Ulrike Eickers |

Deposited On: | 13 Feb 2020 08:38 |

Last Modified: | 27 Feb 2020 13:06 |

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