Numerical Solution of Partial Differential Equations in Modelling Flood Inundation Dynamics in Coastal South West Nigeria

This study develops numerical solutions for the shallow water equations governing flood inundation dynamics in coastal areas of South West Nigeria, applying the finite volume method to simulate the spatial extent and temporal evolution of flood events in the low-lying coastal zone encompassing parts of Lagos, Ogun, and Ondo states. Coastal flooding in this region is driven by a combination of storm surge, tidal effects, and overland flow from intense precipitation events, and the area's rapidly growing coastal population and urban infrastructure are increasingly exposed to flood risk that is expected to intensify under projected climate scenarios. The two-dimensional Saint-Venant shallow water equations are discretised on an unstructured triangular mesh constructed from a 10-metre resolution digital elevation model derived from TanDEM-X satellite radar data. The Roe approximate Riemann solver is implemented within the finite volume discretisation to handle the hyperbolic character of the governing equations and ensure accurate representation of shock-like flood fronts and wet-dry boundary dynamics. Friction and infiltration source terms are incorporated using Manning's roughness coefficients calibrated to land cover data. The model is validated against inundation extent data from the October 2022 coastal flood event derived from Sentinel-1 synthetic aperture radar imagery. Results confirm close agreement between modelled and observed inundation extents for the calibration event, and projections of a 1-in-100-year storm surge scenario are performed. Keywords: shallow water equations, finite volume method, flood inundation, coastal Nigeria, Saint-Venant equations