A two-dimensional well-balanced numerical model for shallow water equations

Modeling flow discontinuities, due to a numerical approach, often pose severe challenges. inthis way, a number of techniques like artificial viscosity (particularly for finite difference methods), shockfitting and etc. have been proposed. these techniques usually require ad-hoc terms which need to beadjusted through calibration. in this study, an efficient numerical model based on a shallow water equationis developed. the model uses a first-order centered (force) scheme, in combination with the surfacegradient method, (sgm) for spatial discretization, and the third order rungekutta algorithm for timeintegration. at first, it is demonstrated that the model is well-balanced, then, through several classicalexamples, such as a 1d dam-break on both dry and wet beds, transcritical flow over a bump, with andwithout shock, sub-critical flow over a bump, circular dam-break, small perturbation propagation, dam-break on a dry bed channel with varying widths and right-angled channel junctions, it is shown thatthe model is capable of capturing flow discontinuities. furthermore, the model can simulate dry bedconditions, and also presents smooth symmetric results.