Reformulation of 2D DG2 Scheme for Shallow Water Modelling

8 pages•Published: September 20, 2018

Abstract

This paper presents a reformulation of the 2D second-order discontinuous Galerkin scheme (2D DG2) which is more efficient and stable for realistic simulation of hydrodynamics. This modified scheme is formulated based on a local linear solution spanned by a set of local coefficients using a newly proposed cell stencil. The results show that the reformulated second-order discontinuous Galerkin scheme performs acceptably well in predicting shock propagation. The modified scheme is designed to be conservative not only for the average coefficients but also the slope coefficients, which is necessary to ensure robustness based on the well-balanced property under the lake at rest hypothesis. Our preliminary findings reveal a great potential from adopting the proposed 2D DG2 reformulation as a basis for real-world flood modelling applications.

Keyphrases: Discontinuous Galerkin, local cell stencil, reformulation, shallow water equations

In: Goffredo La Loggia, Gabriele Freni, Valeria Puleo and Mauro De Marchis (editors). HIC 2018. 13th International Conference on Hydroinformatics, vol 3, pages 131--138

Links:	https://easychair.org/publications/paper/lg4d
	https://doi.org/10.29007/xlvx