Applicability of the local inertial approximation of the shallow water equations to flood modeling

Abstract

Recent studies have demonstrated the improved computational performance of a computer algorithm based on a simplification of the shallow water equations—the so‐called local inertial approximation—which has been observed to provide results comparable to the full set of equations in a range of flood flow problems. This study presents an extended view on the local inertial system, shedding light on those key elements necessary to understand its applicability to flows of practical interest. First, the properties of the simplified system with potential impact on the accuracy of the solutions are described and compared to the corresponding full‐dynamic counterparts. In light of this discussion, the behavior of the solutions is then analyzed through a set of rigorously designed test cases in which analytical solutions to the shallow water system are available. Results show a general good agreement between the local inertial and full‐dynamic models, especially in the lower range of subcritical flows (Fr < 0.5). In terms of steady nonuniform flow water profiles, the error introduced by the local inertial approximation leads to milder water depth gradients, which results in attenuated spatial changes in depth. In unsteady problems, the local inertial approximation leads to slower flood propagation speeds than those predicted by the full‐dynamic equations. Even though our results suggest that the magnitude of these errors is small in a range of floodplain and lowland channels, it becomes increasingly relevant with increasing Fr and depth gradients.