Comparison of numerical schemes for modelling supercritical and transcritical flows along urban floodplains

Many urban floodplains have irregular geometry due to different obstacles and slope conditions. This may change the flow regime from subcritical to supercritical flow conditions, and vice versa. The 1D and 2D shallow water equations (SWEs) that describe these flow conditions are composed of the continuity and momentum equations. The momentum equation is composed of the inertia terms (local and convective acceleration terms), pressure term, gravity term and friction term. Theoretically, in supercritical flows, it is important not to ignore the convective acceleration terms as these terms better express these types of flows. However, the implementation of these terms is not trivial especially in mixed flow conditions as subcritical and supercritical flows require different boundary conditions and hence different solution algorithms. As a matter of fact, this work tries to investigate more on the effect of neglecting the convective acceleration terms by testing four 1D and two 2D models which handle this problem in different ways. In case of 1D modelling, when the flow is supercritical, one of the models implements the full SWEs, the other implements SWEs which completely reduce the convective acceleration terms, the third one implements SWEs which reduce the convective acceleration term partially and the fourth one implements the SWEs by freezing the slope of the negative characteristic curve to some negative value when the Froude number is greater than some critical value. In case of 2D modelling, one of the models uses the full equations whereas the other completely ignores the convective acceleration terms for all kinds of flows. The performance of the modelling tools is then tested by setting up hypothetical case studies which somehow represent features of urban floodplains. The results of the simulations are compared each other by setting the solutions of the methods that solve the full equations as a reference. Findings of the numerical tests in both 1D and 2D cases show that, in most cases, results of models which implement the convective acceleration terms partially or fully or freeze the negative characteristic are very similar compared to solutions of models which implement the full SWEs equations. Hence, the use of full SWEs is not a hard and fast rule in modelling urban floodplains. It rather depends on the situation even if supercritical states dominate the flow. Besides, it also depends on the objective of the modelling work