A New Mass Lumping Scheme for the Mixed Hybrid Finite Element Method: Application to unsaturated water flow modelling
2006
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).
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