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Locally Limited and Fully Conserved RKDG2 Shallow Water Solutions with Wetting and Drying

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Abstract

This work extends a well-balanced second-order Runge-Kutta discontinuous Galerkin (RKDG2) scheme to provide conservative simulations for shallow flows involving wetting and drying over irregular topographies with friction effects. For this purpose, a wetting and drying technique designed originally for a finite volume (FV) scheme is improved and implemented, which includes the discretization of friction source terms via a splitting implicit integration approach. Another focus of this work is to design a fully conserved RKDG2 scheme to provide conservative solutions for both mass and momentum through a local slope limiting process. Several steady and transient benchmark tests with/without friction effects are simulated to validate the new solver and demonstrate the effects of different slope limiting processes, i.e. globally and locally slope limiting processes.

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  1. School of Civil Engineering and Geosciences, Newcastle University, Newcastle upon Tyne, NE1 7RU, England, UK

    Georges Kesserwani & Qiuhua Liang

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  1. Georges Kesserwani
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  2. Qiuhua Liang
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Kesserwani, G., Liang, Q. Locally Limited and Fully Conserved RKDG2 Shallow Water Solutions with Wetting and Drying. J Sci Comput 50, 120–144 (2012). https://doi.org/10.1007/s10915-011-9476-4

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