* @param problem an object of class Dumux::TransportProblem or derived
* @param preComput if preCompute = true previous calculated mobilities are taken, if preCompute = false new mobilities will be computed (for implicit Scheme)
* where \f$S_\alpha\f$ is the saturation of phase alpha (wetting (w), non-wetting (n)) and \f$\boldsymbol{v}_\alpha\f$ is the phase velocity calculated by the multi-phase Darcy equation,
* and of the form
* where \f$S_\alpha\f$ is the saturation of phase alpha (wetting (\f$ w \f$), non-wetting (\f$ n \f$)) and \f$\boldsymbol v_\alpha\f$ is the phase velocity defined by the multi-phase Darcy equation.
* If a phase velocity is reconstructed from the pressure solution it can be directly inserted in the previous equation. In the incompressible case the equation is further divided by the phase density \f$ \rho_\alpha \f$. If a total velocity is reconstructed the saturation equation is reformulated into:
*
* \f[\frac{\partial S_w}{\partial t} + f_w \text{div}\, \boldsymbol{v}_{t} + f_w \lambda_n \boldsymbol{K}\left(\text{grad}\, p_c + (\rho_n-\rho_w) g \text{grad} z \right)= q_\alpha,\f]
* if the non-wetting phase saturation is the primary transport variable.
*
* \f[\frac{\partial S_n}{\partial t} + f_n \text{div}\, \boldsymbol{v}_{t} - f_n \lambda_w \boldsymbol{K}\left(\text{grad}\, p_c + (\rho_n-\rho_w) g \text{grad} z \right)= q_\alpha,\f]
* The total velocity formulation is only implemented for incompressible fluids and \f$ f_\alpha \f$ is the fractional flow function, \f$ \lambda_\alpha \f$ is the mobility, \f$ \boldsymbol K \f$ the absolute permeability,
* \f$ p_c \f$ the capillary pressure, \f$ \rho \f$ the fluid density, \f$ g \f$ the gravity constant, and \f$ q \f$ the source term.
*
* where \f$f_\alpha\f$ is the fractional flow function, \f$\lambda_\alpha\f$ is the mobility, \f$\boldsymbol{K}\f$ the absolute permeability,
* \f$p_c\f$ the capillary pressure, \f$\rho\f$ the fluid density, \f$g\f$ the gravity constant, and \f$q\f$ the source term.
*
* In the IMPES models the default setting is:
*
* - formulation: \f$ p_w-S_w \f$ (Property: <tt>Formulation</tt> defined as <tt>DecoupledTwoPCommonIndices::pwSw</tt>)
* - compressibility: disabled (Property: <tt>EnableCompressibility</tt> set to <tt>false</tt>)
*
* \tparam TypeTag The Type Tag
*/
...
...
@@ -150,22 +163,27 @@ class FVSaturation2P: public FVTransport<TypeTag>
//! Update the values of the material laws and constitutive relations.
/*!
* Constitutive relations like capillary pressure-saturation relationships, mobility-saturation relationships... are updated and stored in the variable class
* of type Dumux::VariableClass2P. The update has to be done when new saturation are available.
*/
// Update the values of the material laws and constitutive relations.
voidupdateMaterialLaws();
/* \brief Writes the current values of the primary transport variable into the <tt>transportedQuantity</tt>-vector (comes as function argument)
