Variational inequalities for modeling flow in heterogeneous porous media with entry pressure |
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Authors: | R Helmig A Weiss B I Wohlmuth |
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Institution: | 1. IWS, Department of Hydromechanics and Modeling of Hydrosystems, Universit?t Stuttgart, Pfaffenwaldring 61, 70529, Stuttgart, Germany 2. Institute of Applied Analysis and Numerical Simulations (IANS), Universit?t Stuttgart, Pfaffenwaldring 57, 70529, Stuttgart, Germany
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Abstract: | One of the driving forces in porous media flow is the capillary pressure. In standard models, it is given depending on the
saturation. However, recent experiments have shown disagreement between measurements and numerical solutions using such simple
models. Hence, we consider in this paper two extensions to standard capillary pressure relationships. Firstly, to correct
the nonphysical behavior, we use a recently established saturation-dependent retardation term. Secondly, in the case of heterogeneous
porous media, we apply a model with a capillary threshold pressure that controls the penetration process. Mathematically,
we rewrite this model as inequality constraint at the interfaces, which allows discontinuities in the saturation and pressure.
For the standard model, often finite-volume schemes resulting in a nonlinear system for the saturation are applied. To handle
the enhanced model at the interfaces correctly, we apply a mortar discretization method on nonmatching meshes. Introducing
the flux as a new variable allows us to solve the inequality constraint efficiently. This method can be applied to both the
standard and the enhanced capillary model. As nonlinear solver, we use an active set strategy combined with a Newton method.
Several numerical examples demonstrate the efficiency and flexibility of the new algorithm in 2D and 3D and show the influence
of the retardation term.
This work was supported in part by IRTG NUPUS. |
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Keywords: | Porous media Entry pressure Variational inequality Mortar Active set strategy |
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