Speaker
Description
The Richards equation, a nonlinear elliptic–parabolic equation, is widely used to describe infiltration in porous media. We present a finite element method for solving the Richards equation by introducing a bounded auxiliary variable that removes unbounded terms from the weak formulation. The formulation is discretized with a semi-implicit scheme, and the resulting nonlinear system is solved using Newton’s method. This approach eliminates the need for regularization techniques and provides advantages in handling both dry and fully saturated zones. A non-overlapping Schwarz domain decomposition method is employed for modeling infiltration in layered soils. The proposed method is tested using the van Genuchten models for capillary pressure. Numerical experiments are performed to validate the approach, including flows in fibrous sheets with initially dry media, cases with both saturated and dry regions, and infiltration in layered soils. The results demonstrate the stability and accuracy of the method, with numerical solutions remaining positive even in completely dry zones. The simulations confirm the ability of the proposed approach to predict the dynamics of unsaturated flow in soils effectively.
| References | Benfanich, A., Bourgault, Y., & Beljadid, A. (2025). A finite element method using a bounded auxiliary variable for solving the Richards equation. arXiv:2510.13012 [math.NA]. https://doi.org/10.48550/arXiv.2510.13012 |
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| Country | Canada |
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