Compositional Multi-Phase Model Directly Solving Non-linear Complementarity Problems. More...
Classes | |
class | Ewoms::NcpBoundaryRateVector< TypeTag > |
Implements a boundary vector for the fully implicit compositional multi-phase NCP model. More... | |
class | Ewoms::NcpExtensiveQuantities< TypeTag > |
This template class represents the extensive quantities of the compositional NCP model. More... | |
struct | Ewoms::NcpIndices< TypeTag, PVOffset > |
The primary variable and equation indices for the compositional multi-phase NCP model. More... | |
class | Ewoms::NcpIntensiveQuantities< TypeTag > |
Contains the quantities which are are constant within a finite volume in the compositional multi-phase NCP model. More... | |
class | Ewoms::NcpLocalResidual< TypeTag > |
Details needed to calculate the local residual in the compositional multi-phase NCP-model . More... | |
class | Ewoms::NcpModel< TypeTag > |
A compositional multi-phase model based on non-linear complementarity functions. More... | |
class | Ewoms::NcpNewtonMethod< TypeTag > |
A Newton solver specific to the NCP model. More... | |
class | Ewoms::NcpPrimaryVariables< TypeTag > |
Represents the primary variables used by the compositional multi-phase NCP model. More... | |
class | Ewoms::NcpRateVector< TypeTag > |
Implements a vector representing mass, molar or volumetric rates. More... | |
Compositional 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 FluxModule
property. For example, the velocity model can by changed to the Forchheimer approach by
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: