An efficient lumped mixed hybrid finite element formulation for variably saturated groundwater flow

Benjamin Belfort, Fanilo Ramasomanana, Anis Younes, François Lehmann

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12 Citations (Scopus)


Accurate numerical simulation of infi ltration in the vadose zone remains a challenge, especially when very sharp fronts are modeled. In this work, we used the mixed hybrid fi nite element (MHFE) method, which allows a simultaneous approximation of both pressure head and velocity and can handle general irregular grids with highly heterogeneous permeability. For many problems dealing with unsaturated water fl ow, however, the MHFE solutions exhibit signifi cant unphysical oscillations. To avoid this phenomenon, we developed an effi cient mass-lumping scheme with the MHFE method for solving the mixed form of the Richards equation. In this work, the standard and lumped MHFE formulations were compared and the ability of the lumped formulation to reduce unphysical oscillations was determined for oneand two-dimensional infi ltration problems. Theoretical analysis based on the M-matrix property, which guarantees the discrete maximum principle, and practical test cases performed in this study underline the advantage of using an acute triangulation to completely remove the unphysical oscillations. Indeed, contrary to the standard approach, the lumped formulation satisfi es the M-matrix property without any constraint on the time step size to be used.

Original languageEnglish
Pages (from-to)352-362
Number of pages11
JournalVadose Zone Journal
Issue number2
Publication statusPublished - 1 May 2009


ASJC Scopus subject areas

  • Soil Science

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