Depth integrated equations applied to longitudinal discontinuities on the channel bed

Razmand, Maral
Depth integrated equations can be solved over large domains to provide flood inundation maps. In urban and rural areas however, there may be numerous natural or artificial bottom boundary discontinuities in the form of rapid variations in the bed elevation. Such discontinuities cause abrupt changes in the source terms of the governing equations and can significantly affect stability and accuracy of the numerical solution. A 1D code is developed for shallow water equations using HLL approximate Riemann solver. It is applied to a dam-break case until the steady state is reached between two end boundaries and volume conserving boundary conditions has been searched. Channel beds with step-like discontinuities were also studied. It is found that bed slopes greater than 1 can cause spurious water surface oscillations in the numerical solution.