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Journal of Scientific Computing

, Volume 50, Issue 1, pp 120–144 | Cite as

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

  • Georges Kesserwani
  • Qiuhua LiangEmail author
Article

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.

Keywords

Discontinuous Galerkin method Local slope-limiter vs. global slope-limiter Wetting and drying Irregular topography Friction term discretization Conservative scheme 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.School of Civil Engineering and GeosciencesNewcastle UniversityNewcastle upon TyneEngland, UK

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