High-resolution finite-volume method for shallow water flows

A high-resolution time-marching method is presented for solving the two-dimensional shallow water equations. The method uses a cell-centered formulation with collocated data rather than a space-staggered approach. Spurious oscillations are avoided by employing Monotonic Upstream Schemes for Conservation Laws (MUSCL) reconstruction with an approximate Riemann solver in a two-step Runge-Kutta time stepping scheme. A finite-volume implementation on a boundary conforming mesh is chosen to more accurately map the complex geometries that will occur in practice. These features enable the model to deal with dam break phenomena involving flow discontinuities, subcritical and supercritical flows, and other cases. The method is applied to several bore wave propagation and dam break problems.