TY - JOUR
T1 - Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds
AU - Bollermann , Andreas
AU - Noelle , Sebastian
AU - Lukáčová-Medvid'ová , Maria
JO - Communications in Computational Physics
VL - 2
SP - 371
EP - 404
PY - 2011
DA - 2011/10
SN - 10
DO - http://doi.org/10.4208/cicp.220210.020710a
UR - https://global-sci.org/intro/article_detail/cicp/7446.html
KW - 
AB - <p style="text-align: justify;">We 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. Well-balancing
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.</p>