A New Mass Lumping Scheme for the Mixed Hybrid ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

A New Mass Lumping Scheme for the Mixed Hybrid Finite Element Method: Application to unsaturated water flow modelling
Paper
Author:BENJAMIN BELFORT <bbelfort@imfs.u-strasbg.fr> (Institut de Mecanique des Fluides et des Solides de Strasbourg)
FRANCOIS LEHMANN <lehmann@imfs.u-strasbg.fr> (Institut de Mecanique des Fluides et des Solides de Strasbourg)
ANIS YOUNES <younes@imfs.u-strasbg.fr> (Institut de Mecanique des Fluides et des Solides de Strasbourg)
PHILIPPE ACKERER <ackerer@imfs.u-strasbg.fr> (Institut de Mecanique des Fluides et des Solides de Strasbourg)
Presenter:BENJAMIN BELFORT <bbelfort@imfs.u-strasbg.fr> (Institut de Mecanique des Fluides et des Solides de Strasbourg)
Date: 2006-06-18     Track: General Sessions     Session: General
DOI:10.4122/1.1000000514
DOI:10.4122/1.1000000515

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).