On the Refinement of a Boundary-Fitted Shallow Water Model

Abstract

The two-dimensional shallow water equations were formulated and numerically solved in an arbitrary curvilinear coordinate system, which offers a relatively high degree of flexibility in representing the natural flow domains with structured meshes. The model employs an efficient TVD-MacCormack scheme, which has second-order accuracy in both time and space. Refinements were made to enhance the model's accuracy and stability in computing the shallow wave dynamics in real-world scenarios, with irregular boundaries and uneven beds. In particular, advanced open boundary conditions have been proposed according to the method of characteristics, and rigorous mass conservation has been enforced during the computation at both the inner-domain and the boundaries. These refinements are necessary when modeling the flood inundation over a large area and the tidal oscillation in a macro-tidal estuary. The effectiveness of the refinements was verified by simulating the forced tidal resonance in an idealized condition and the Malpasset dam-break flood in the Reyran river valley. The application of the refined model in the study of tidal oscillations in the Severn Estuary and Bristol Channel can be found in the companion paper.