TY - JOUR
T1 - Robust a Simulation for Shallow Flows with Friction on Rough Topography
AU - Jian Deng, Ruo Li, Tao Sun & Shuonan Wu
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 384
EP - 407
PY - 2013
DA - 2013/06
SN - 6
DO - http://doi.org/10.4208/nmtma.2013.1129nm
UR - https://global-sci.org/intro/article_detail/nmtma/5910.html
KW - Shallow water, free interface, Manning force.
AB - <p style="text-align: justify;">In this paper, we propose a robust finite volume scheme to numerically solve
the shallow water equations on complex rough topography. The major difficulty of this
problem is introduced by the stiff friction force term and the wet/dry interface tracking.
An analytical integration method is presented for the friction force term to remove the
stiffness. In the vicinity of wet/dry interface, the numerical stability can be attained by
introducing an empirical parameter, the water depth tolerance, as extensively adopted
in literatures. We propose a problem independent formulation for this parameter, which
provides a stable scheme and preserves the overall truncation error of $\mathbb{O}$∆$x^3$. The
method is applied to solve problems with complex rough topography, coupled with $h$-adaptive mesh techniques to demonstrate its robustness and efficiency.</p>