zeroInertiaFlowFOAM – a OpenFOAM®-based computationally efficient, mass-conservative, implicit zero-inertia flow model for flood inundation problems on collocated grid-systems.

The diffusive wave or the zero-inertia (ZI) model for surface runoff modeling is derived by neglecting the local and convective acceleration terms from the two-dimensional (2D) depth-averaged shallow water equations (SWE). The ZI model is computationally efficient and highly accurate compared to the SW models for modeling low subcritical (Froude number < 0.5) flood propagation problems. The current study presents a Finite Volume (FV) method-based ZI flow model – zeroInertiaFlowFOAM, developed using the OpenFOAM^® framework [1]. The model utilizes the implicit time discretization scheme and the Picard iteration scheme for the linearization of the non-linear momentum equation. The stabilized and adaptive time-stepping algorithm implemented in the present model adjusts the future time step size based on the convergence characteristics of the iterative scheme at the present time step, thereby enhancing the computational efficiency. The existing ZI model – surfaceFlowFOAM [2] suffered from high mass balance errors (MBE) and chequerboard oscillations while simulating flood flows due to high rainfall intensities over surfaces with steep bed-slopes. The present model is a modified version of surfaceFlowFOAM. In the present model, the velocity is calculated from the momentum equation at the element centroids of the collocated grid-system. The calculated velocity is used to solve the continuity equation, where the divergence of the flux term is discretized using the upwind scheme. This relates the gradient of the flow depth (∇h) to the values at the consecutive element centroids, thereby eliminating the possibility of chequerboard instability arising in the regions where the water-surface slope changes sharply. It significantly reduces the restrictions on mesh generation for such problems, thereby increasing the computational efficiency when compared to surfaceFlowFOAM. Moreover, the modified discretization technique adopted in zeroInertiaFlowFOAM has helped in achieving high mass balance accuracy which was another significant limitation in surfaceFlowFOAM. The applicability of zeroInertiaFlowFOAM has also been verified and validated against the standard benchmark problems from the literature.

References

[1] Jasak, H., A. Jemcov, Z. Tukovic. (2007). OpenFOAM: A C++ library for complex physics simulations. In Vol. 1000 of Proc., Int. Workshop on Coupled Methods in Numerical Dynamics,1–20. Dubrovnik, Croatia: Inter-University Center

[2] Dey, S., Dhar, A. (2024). Applicability of Zero-Inertia Approximation for Overland Flow Using a Generalized Mass-Conservative Implicit Finite Volume Framework. Journal of Hydrologic Engineering, 29(1), 04023042.