Applicability of Zero-Inertia Approximation for Overland Flow Using a Generalized Mass-Conservative Implicit Finite Volume Framework

Abstract

The zero-inertia approximation of the shallow water equations has been observed to provide reasonably accurate results for various flood propagation problems. The commonly adopted explicit time schemes in the numerical modeling of zero-inertia flows are computationally expensive and vulnerable to numerical instabilities. This paper presents a finite volume method-based zero-inertia overland flow model named surfaceFlowFOAM, developed using OpenFOAM framework with an implicit time discretization scheme. The nonlinear zero-inertia equation is linearized by applying the iterative Picard linearization technique. We have implemented a stabilized and adaptive time-stepping algorithm for controlling the convergence of Picard iterations to avoid numerical instability, thereby enhancing the overall computational efficiency. This study analyzes that the applicability of the zero-inertia approximation should be limited to low subcritical surface flow problems with Froude numbers less than 0.5. The analysis has been done by observing the effects of variations in bed-slope and rainfall intensity on the Froude number of flows developing over the overland surface. Furthermore, we have discussed the achieved mass balance accuracy of surfaceFlowFOAM in solving the considered test examples. The numerical results of surfaceFlowFOAM show excellent correspondence with the results presented in the literature for solved overland flow problems. The solution accuracy and the achieved computational efficiency ensure the potential applicability of surfaceFlowFOAM to solve the lower range (Froude number <0.5) of two-dimensional subcritical flood flow problems.