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Description
The aim of this work is to accurately reproduce hydraulic interactions between ocean waves and watersheds over large spatial and temporal scales (from meters to kilometers and from minutes to days). This modeling is essential for reliable numerical simulations that can be used for regional forecasts in the context of climate change, particularly regarding water resources and morphodynamic processes. The problem of surface water infiltration into the unsaturated zone, known as the vadose zone, appears to be the main obstacle to the reliability of such predictions, as it plays a key role in the hydraulic response of a watershed (Ersoy, 2021).
Among existing models, the Richards equation makes it possible to capture both saturated and vadose zones simultaneously. The first part of this work focused on assessing the implementation of this equation in the massively parallel 3D cartesian Finite Volume Notus CFD code (Notus, 2024). The equation is highly non-linear for large non-homogeneous soils and therefore requires a Newton solver, which has been implemented. Both hydraulic head and water content formulations of the Richards equation have been investigated along with adapted numerical schemes.
We validated the numerical strategy on several test cases (Clement, 2021), ranging from capillary-dominated to large-scale gravity-driven flows.
Within this framework, more realistic configurations have been considered, including heterogeneous soils with strong contrasts in hydraulic properties and saturation effects over immersed obstacles.
The code can effectively be used to reproduce a wide range of applications involving porous media infiltration and exfiltration.
In future work, the coupling of the vadose zone with air and water at the interface will be investigated through adapted boundary conditions, allowing interactions with the two-phase Navier–Stokes solution, whether the porous medium receives mass (infiltration) or releases it (exfiltration). Particular attention will be given to numerical methods ensuring mass and energy conservation at the interface between the two models. Finally, the code will be compared with complex experimental benchmarks such as the La Verne Dam case (Fleureau, 1991).
| References | [1] M. Ersoy and al, "A Saint-Venant Model for Overland Flows with Precipitation and Recharge", Mathematical and Computational Applications, vol. 26, no. 1, 2021, doi: 10.3390/mca26010001 [2] Notus CFD, v0.6.0, https://notus-cfd.org, 2024 [3] J.-B. Clément, "Numerical simulation of flows in unsaturated porous media by an adaptive discontinuous Galerkin method: application to sandy beaches", University of Toulon, 2021, tel-03121283 [4] J. M. Fleureau and al, "Validation des modèles de couplage sur ouvrage réels", scientific report from GRECO, 1991 |
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| Country | France |
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