In this paper we propose a new numerical scheme to simulate the river flow in the presence of a variable bottom surface. We use the finite volume method, our approach is based on the technique described by D. L. George for shallow water equations. The main goal is to construct the scheme, which is well balanced, i.e. maintains not only some special steady states but all steady states which can occur. Furthermore this should preserve nonnegativity of some quantities, which are essentially nonnegative from their physical fundamental, for example the cross section or depth. Our scheme can be extended to the second order accuracy.
@article{702853,
title = {Numerical modelling of river flow (numerical schemes for one type of nonconservative systems},
booktitle = {Programs and Algorithms of Numerical Mathematics},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2008},
pages = {23-36},
zbl = {05802239},
url = {http://dml.mathdoc.fr/item/702853}
}
Brandner, Marek; Egermaier, Jiří; Kopincová, Hana. Numerical modelling of river flow (numerical schemes for one type of nonconservative systems, dans Programs and Algorithms of Numerical Mathematics, GDML_Books, (2008), pp. 23-36. http://gdmltest.u-ga.fr/item/702853/