@Article{CiCP-7-5,
author = {},
title = {A Well-Balanced and Non-Negative Numerical Scheme for Solving the Integrated Shallow Water and Solute Transport Equations},
journal = {Communications in Computational Physics},
year = {2010},
volume = {7},
number = {5},
pages = {1049--1075},
abstract = {<p style="text-align: justify;">Based on the recent development in shallow flow modelling, this paper
presents a finite volume Godunov-type model for solving a 4×4 hyperbolic matrix
system of conservation laws that comprise the shallow water and depth-averaged solute
transport equations. The adopted governing equations are derived to preserve
exactly the solution of lake at rest so that no special numerical technique is necessary
in order to construct a well-balanced scheme. The HLLC approximate Riemann solver
is used to evaluate the interface fluxes. Second-order accuracy is achieved using the
MUSCL slope limited linear reconstruction together with a Runge-Kutta time integration
method. The model is validated against several benchmark tests and the results
are in excellent agreement with analytical solutions or other published numerical predictions.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.2009.09.156},
url = {https://global-sci.com/article/81015/a-well-balanced-and-non-negative-numerical-scheme-for-solving-the-integrated-shallow-water-and-solute-transport-equations}
}