Derivation of weakly hydrodynamic models in the Dupuit-Forchheimer regime
Résumé
The current study is dedicated to the formal derivation of a hierarchic of asymp- totic models that approximate the groundwater wave problem within the Dupuit- Forchheimer regime, over a regular, non-planar substratum. The derivation methodology employed bears resemblance to the techniques utilized in hier- archic of asymptotic models for approximating the water waves problem in the shallow water regime. Mathematically speaking, the asymptotic models mani- fest as nonlinear, non-local diffusion equations. We identify an energy dissipa- tion law inherent to these models, thereby bolstering the physical validity and confidence in the proposed framework. A numerical strategy is proposed that preserved at the discrete level the energy dissipation. Several simulations are conducted to discuss and validate the dynamic behavior of the solution.
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