Fully coupled generalised hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part II: numerical scheme and numerical results |
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| Authors: | Estelle Marchand Torsten Müller Peter Knabner |
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| Institution: | 1.Department of Mathematics, Applied Mathematics 1,University of Erlangen-Nuremberg,Erlangen,Germany |
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| Abstract: | We consider the modeling and simulation of compositional two-phase flow in a porous medium, where one phase is allowed to
vanish or appear. The modeling of Marchand et al. (in review) leads to a nonlinear system of two conservation equations. Each
conservation equation contains several nonlinear diffusion terms, which in general cannot be written as a function of the
gradients of the two principal unknowns. Also the diffusion coefficients are not necessarily explicit local functions of them.
For the generalised mixed finite elements approximation, Lagrange multipliers associated to each principal unknown are introduced,
the sum of the diffusive fluxes of each component is explicitly eliminated and the static condensation leads to a “global”
nonlinear system of equations only in the Lagrange multipliers also including complementarity conditions to cope with vanishing
or appearing phases. After time discretisation, this system can be solved at each time step using a semi-smooth Newton method.
The static condensation involves “local” nonlinear systems of equations associated to each element, solved also by a semismooth
Newton method. The algorithm is successfully applied to 1D and 2D examples of water–hydrogen flow involving gas phase appearance
and disappearance. |
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