François Lehmann

Modélisation du transport d'un soluté réactif en milieux poreux non saturés

Abstract Solute transfer in soils may create sharp concentration fronts. The numerical modeling of these fronts remains a difficult problem. The proposed one-dimensional model (Wamos-T) is robust and well adapted to these problems. It is based on operator splitting: discontinuous finite elements combined with a slope limiting procedure is used to discretize the advective term, the dispersive and reactive terms of the transport equation being solved by an implicit finite differences scheme. Compared to a widely used finite element method (Hydrus-1D), Wamos-T provides more accurate results when sharp fronts occur.

A New Mass Lumping Scheme for the Mixed Hybrid Finite Element Method: Application to unsaturated water flow modelling

Abstract: Groundwater flow modelling is of interest in many sciences and engineering applications for scientific understanding and/or technological management. Accurate numerical simulation of infiltration in the vadose zone remains a challenge, especially when very sharp fronts are present. This study is focused principally on an alternatively numerical approaches referred to in the literature as the mixed hybrid finite element (MHFE) method. MHFE schemes simultaneously approximate both the pressure head and its gradient. For some problems of unsaturated water flow, the MHFE solutions contain oscillations. Various authors ( see [1]) suggest the use of a mass lumping procedure to avoid this unphysical phenomenon. An analyse of the resulting matrix system shows that the recommended technique differs from the standard mass-lumping well-established for Galerkin finite element methods. A “new” effective mass-lumping scheme adapted from [2] has been specially developed for the MHFE method. Its ability for eliminating oscillations have been tested in unsaturated conditions. Various test cases in a 2D domain, for homogeneous and heterogeneous dry porous media and subject to different boundary conditions are presented. References: [1] Farthing, M. W., C. E. Kees, and C. T. Miller. 2003. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv. Water Resour. 26:373-394. [2] Younes A., Ackerer P. and Lehmann F., 2005.A new mass lumping scheme for the mixed hybrid finite element method, Int. J. Numer. Meth. Engng. (submitted).