scholarly journals Comparison study of some finite volume and finite element methods for the shallow water equations with bottom topography and friction terms

2006 ◽  
Vol 86 (11) ◽  
pp. 874-891 ◽  
Author(s):  
M. Lukáčová-Medvid'ová ◽  
U. Teschke
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Finite Volume ◽  
Finite Element Methods ◽  
Shallow Water Equations ◽  
Bottom Topography ◽  
Comparison Study

scholarly journals Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds

2011 ◽  
Vol 10 (2) ◽  
pp. 371-404 ◽  
Author(s):  
Andreas Bollermann ◽  
Sebastian Noelle ◽  
Maria Lukáčová-Medvid’ová
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Bottom Topography ◽  
Main Idea ◽  
Rarefaction Waves ◽  
Finite Volume Schemes ◽  
A Cell ◽  
Gravity Driven ◽  
Water Height

AbstractWe present a new Finite Volume Evolution Galerkin (FVEG) scheme for the solution of the shallow water equations (SWE) with the bottom topography as a source term. Our new scheme will be based on the FVEG methods presented in (Noelle and Kraft, J. Comp. Phys., 221 (2007)), but adds the possibility to handle dry boundaries. The most important aspect is to preserve the positivity of the water height. We present a general approach to ensure this for arbitrary finite volume schemes. The main idea is to limit the outgoing fluxes of a cell whenever they would create negative water height. Physically, this corresponds to the absence of fluxes in the presence of vacuum. Wellbalancing is then re-established by splitting gravitational and gravity driven parts of the flux. Moreover, a new entropy fix is introduced that improves the reproduction of sonic rarefaction waves.

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