NCP Compositional Multi-Phase Model Directly Solving Non-linear Complementarity Problems. More...
Collaboration diagram for NCP:
Detailed DescriptionCompositional Multi-Phase Model Directly Solving Non-linear Complementarity Problems. This model implements a -phase flow of a fluid mixture composed of chemical species. The phases are denoted by lower index . All fluid phases are mixtures of chemical species which are denoted by the upper index . By default, the standard multi-phase Darcy approach is used to determine the velocity, i.e.
although the actual approach which is used can be specified via the SET_TYPE_PROP(MyProblemTypeTag, FluxModule, Ewoms::ForchheimerFluxModule<TypeTag>);
The core of the model is the conservation mass of each component by means of the equation
For the missing model assumptions, the model uses non-linear complementarity functions. These are based on the observation that if a fluid phase is not present, the sum of the mole fractions of this fluid phase is smaller than , i.e.
Also, if a fluid phase may be present at a given spatial location its saturation must be non-negative:
Since at any given spatial location, a phase is always either present or not present, one of the strict equalities on the right hand side is always true, i.e.
always holds. These three equations constitute a non-linear complementarity problem, which can be solved using so-called non-linear complementarity functions . Such functions have the property
Several non-linear complementarity functions have been suggested, e.g. the Fischer-Burmeister function
This model uses
because of its piecewise linearity. The model assumes local thermodynamic equilibrium and uses the following primary variables:
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