TY - JOUR
T1 - Momentum Conservative Schemes for Shallow Water Flows
AU - S. R. Pudjaprasetya & I. Magdalena
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 152
EP - 165
PY - 2018
DA - 2018/02
SN - 4
DO - http://doi.org/10.4208/eajam.290913.170314a
UR - https://global-sci.org/intro/article_detail/eajam/10829.html
KW - Finite volume method, staggered grid, conservative scheme, shallow water equations.
AB - <p style="text-align: justify;">We discuss the implementation of the finite volume method on a staggered
grid to solve the full shallow water equations with a conservative approximation for
the advection term. Stelling &amp; Duinmeijer [15] noted that the advection approximation
may be energy-head or momentum conservative, and if suitable which of these to
implement depends upon the particular flow being considered. The momentum conservative
scheme pursued here is shown to be suitable for 1D problems such as transcritical
flow with a shock and dam break over a rectangular bed, and we also found that our
simulation of dam break over a dry sloping bed is in good agreement with the exact
solution. Further, the results obtained using the generalised momentum conservative
approximation for 2D shallow water equations to simulate wave run up on a conical
island are in good agreement with benchmark experimental data.</p>