Displaying similar documents to “A numerical approximation of non-Fickian flows with mixing length growth in porous media.”

Continuous-time finite element analysis of multiphase flow in groundwater hydrology

Zhangxin Chen, Magne Espedal, Richard E. Ewing (1995)

Applications of Mathematics

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A nonlinear differential system for describing an air-water system in groundwater hydrology is given. The system is written in a fractional flow formulation, i.e., in terms of a saturation and a global pressure. A continuous-time version of the finite element method is developed and analyzed for the approximation of the saturation and pressure. The saturation equation is treated by a Galerkin finite element method, while the pressure equation is treated by a mixed finite element method....

A degenerate parabolic system for three-phase flows in porous media

Vladimir Shelukhin (2007)

Annales mathématiques Blaise Pascal

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A classical model for three-phase capillary immiscible flows in a porous medium is considered. Capillarity pressure functions are found, with a corresponding diffusion-capillarity tensor being triangular. The model is reduced to a degenerate quasilinear parabolic system. A global existence theorem is proved under some hypotheses on the model data.

Instability of mixed finite elements for Richards' equation

Březina, Jan

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Richards' equation is a widely used model of partially saturated flow in a porous medium. In order to obtain conservative velocity field several authors proposed to use mixed or mixed-hybrid schemes to solve the equation. In this paper, we shall analyze the mixed scheme on 1D domain and we show that it violates the discrete maximum principle which leads to catastrophic oscillations in the solution.