%0 Journal Article
%A Vázquez-Cendón, M.E.
%A Toro, E.F.
%T Exact solution of some hyperbolic systems with source terms
%D 2003
%R 10.1098/rspa.2002.0987
%J Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
%P 263-271
%V 459
%N 2029
%X In this paper we present a methodology for constructing exact solutions to hyperbolic systems with source or forcing terms. We illustrate the approach as applied to some inhomogeneous systems arising in environmental problems, namely the inhomogeneous linearized shallow–water equations. We solve exactly a generalized Riemann problem that models dam–break problems in channels with variable bottom elevation and variable width. The exact solutions obtained are very valuable in the process of assessing the performance of numerical methods intended for solving more–complex problems; they can also be useful in providing new ideas to be used in the design of numerical methods for more–general inhomogeneous systems.
%U http://rspa.royalsocietypublishing.org/content/royprsa/459/2029/263.full.pdf