Implicit Discontinuous Galerkin Scheme for Discontinuous Bathymetry in Shallow Water Equations

2020 ◽  
Vol 24 (9) ◽  
pp. 2694-2705
Author(s):  
Haegyun Lee
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Shallow Water Equations ◽  
Galerkin Scheme ◽  
Discontinuous Galerkin Scheme

scholarly journals Reformulation of 2D DG2 Scheme for Shallow Water Modelling

10.29007/xlvx ◽  
2018 ◽  
Author(s):  
Janice Ayog ◽  
Georges Kesserwani
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Real World ◽  
Second Order ◽  
Shock Propagation ◽  
Linear Solution ◽  
Galerkin Scheme ◽  
Flood Modelling ◽  
Discontinuous Galerkin Scheme ◽  
Local Coefficients

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.

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