P. Garcia-navarro et Me. Vazquez-cendon, On numerical treatment of the source terms in the shallow water equations, COMPUT FLU, 29(8), 2000, pp. 951-979
Upwind schemes are very well adapted to advection dominated flows and have
become popular for applications involving the Euler system of equations. Re
cently, Riemann solver-based techniques such as Roe's scheme have become a
successful tool for numerical simulation of other conservation laws like th
e shallow water equations. One of the disadvantages of this technique is re
lated to the treatment of the source terms of the equations. The conservati
vity of the scheme can be seriously damaged if a careless treatment is appl
ied. Previous papers studied the way to treat the terms arising from bed le
vel changes. This gaper deals with the analysis of the main reasons leading
to a correct treatment of the geometrical source terms, that is, those rep
resenting the changes in cross-section which may be linked to the specific
dependence of the flux function on the geometry. (C) 2000 Elsevier Science
Ltd. All rights reserved.