diff --git a/doc/handbook/ModelDescriptions/2pdecoupledpressuremodel.tex b/doc/handbook/ModelDescriptions/2pdecoupledpressuremodel.tex index 5e8ce73d1c353274f344058299c21b424fd14424..bffc37b6ae14f718671669ca01af95c1ba1345c2 100644 --- a/doc/handbook/ModelDescriptions/2pdecoupledpressuremodel.tex +++ b/doc/handbook/ModelDescriptions/2pdecoupledpressuremodel.tex @@ -18,7 +18,7 @@ In the I\-M\-P\-E\-S models the default setting is\-: \begin{itemize} -\item formulation\-: $ p_w-S_w $ (Property\-: {\itshape Formulation} defined as {\itshape \hyperlink{a00096_a601a847774d6e1b2e2a2b469f70c3f22}{Decoupled\-Two\-P\-Common\-Indices\-::pwsw}}) +\item formulation\-: $ p_w-S_w $ (Property\-: {\itshape Formulation} defined as {\itshape \hyperlink{a00095_a601a847774d6e1b2e2a2b469f70c3f22}{Decoupled\-Two\-P\-Common\-Indices\-::pwsw}}) \item compressibility\-: disabled (Property\-: {\itshape Enable\-Compressibility} set to {\itshape false}) \end{itemize} diff --git a/doc/handbook/ModelDescriptions/2pdecoupledsaturationmodel.tex b/doc/handbook/ModelDescriptions/2pdecoupledsaturationmodel.tex index 7f121c5bb21ac986e07d7011c3ea45bb6a31ef87..8bf9b712ef2ceafe86eaaadc9ffc8a18c031a691 100644 --- a/doc/handbook/ModelDescriptions/2pdecoupledsaturationmodel.tex +++ b/doc/handbook/ModelDescriptions/2pdecoupledsaturationmodel.tex @@ -16,7 +16,7 @@ The total velocity formulation is only implemented for incompressible fluids and In the I\-M\-P\-E\-S models the default setting is\-: -formulation\-: $ p_w $ -\/ $ S_w $ (Property\-: {\itshape Formulation} defined as {\itshape \hyperlink{a00096_a601a847774d6e1b2e2a2b469f70c3f22}{Decoupled\-Two\-P\-Common\-Indices\-::pwsw}}) +formulation\-: $ p_w $ -\/ $ S_w $ (Property\-: {\itshape Formulation} defined as {\itshape \hyperlink{a00095_a601a847774d6e1b2e2a2b469f70c3f22}{Decoupled\-Two\-P\-Common\-Indices\-::pwsw}}) compressibility\-: disabled (Property\-: {\itshape Enable\-Compressibility} set to {\itshape false}) diff --git a/doc/handbook/ModelDescriptions/co2implicitmodel.tex b/doc/handbook/ModelDescriptions/co2implicitmodel.tex index 80a8d27b742e3cd7d727102ef5b0fdb1fd3875e5..9cf12fd170ace9dcf5bd6e2523c012764657d657 100644 --- a/doc/handbook/ModelDescriptions/co2implicitmodel.tex +++ b/doc/handbook/ModelDescriptions/co2implicitmodel.tex @@ -4,5 +4,5 @@ % file instead!! % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -See \hyperlink{a00557}{Two\-P\-Two\-C\-Model} for reference to the equations used. The \hyperlink{a00072}{C\-O2} model is derived from the 2p2c model. In the \hyperlink{a00072}{C\-O2} model the phase switch criterion is different from the 2p2c model. The phase switch occurs when the equilibrium concentration of a component in a phase is exceeded, instead of the sum of the components in the virtual phase (the phase which is not present) being greater that unity as done in the 2p2c model. The \hyperlink{a00079}{C\-O2\-Volume\-Variables} do not use a constraint solver for calculating the mole fractions as is the case in the 2p2c model. Instead mole fractions are calculated in the Fluid\-System with a given temperature, pressurem and salinity. The model is able to use either mole or mass fractions. The property use\-Moles can be set to either true or false in the problem file. Make sure that the according units are used in the problem setup. use\-Moles is set to false by default. +See \hyperlink{a00591}{Two\-P\-Two\-C\-Model} for reference to the equations used. The \hyperlink{a00073}{C\-O2} model is derived from the 2p2c model. In the \hyperlink{a00073}{C\-O2} model the phase switch criterion is different from the 2p2c model. The phase switch occurs when the equilibrium concentration of a component in a phase is exceeded, instead of the sum of the components in the virtual phase (the phase which is not present) being greater that unity as done in the 2p2c model. The \hyperlink{a00080}{C\-O2\-Volume\-Variables} do not use a constraint solver for calculating the mole fractions as is the case in the 2p2c model. Instead mole fractions are calculated in the Fluid\-System with a given temperature, pressurem and salinity. The model is able to use either mole or mass fractions. The property use\-Moles can be set to either true or false in the problem file. Make sure that the according units are used in the problem setup. use\-Moles is set to false by default. diff --git a/doc/handbook/ModelDescriptions/co2niimplicitmodel.tex b/doc/handbook/ModelDescriptions/co2niimplicitmodel.tex index 3cf083b448fe14e287d9d93309e18a6f44dc4a6d..140b5289804208f824f8aaf5afe375e6c31b6317 100644 --- a/doc/handbook/ModelDescriptions/co2niimplicitmodel.tex +++ b/doc/handbook/ModelDescriptions/co2niimplicitmodel.tex @@ -4,5 +4,5 @@ % file instead!! % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -See Two\-P\-Two\-C\-N\-I model for reference to the equations. The C\-O2\-N\-I model is derived from the \hyperlink{a00072}{C\-O2} model. In the \hyperlink{a00072}{C\-O2} model the phase switch criterion is different from the 2p2c model. The phase switch occurs when the equilibrium concentration of a component in a phase is exceeded instead of the sum of the components in the virtual phase (the phase which is not present) being greater that unity as done in the 2p2c model. The \hyperlink{a00079}{C\-O2\-Volume\-Variables} do not use a constraint solver for calculating the mole fractions as is the case in the 2p2c model. Instead mole fractions are calculated in the Fluid\-System with a given temperature, pressure and salinity. +See Two\-P\-Two\-C\-N\-I model for reference to the equations. The C\-O2\-N\-I model is derived from the \hyperlink{a00073}{C\-O2} model. In the \hyperlink{a00073}{C\-O2} model the phase switch criterion is different from the 2p2c model. The phase switch occurs when the equilibrium concentration of a component in a phase is exceeded instead of the sum of the components in the virtual phase (the phase which is not present) being greater that unity as done in the 2p2c model. The \hyperlink{a00080}{C\-O2\-Volume\-Variables} do not use a constraint solver for calculating the mole fractions as is the case in the 2p2c model. Instead mole fractions are calculated in the Fluid\-System with a given temperature, pressure and salinity. diff --git a/doc/handbook/ModelDescriptions/mpncimplicitmodel.tex b/doc/handbook/ModelDescriptions/mpncimplicitmodel.tex index bcdc19339173ea125b6e2e1ef2391582686b6a2b..ebd4339c8964259bc3a759ff46a0c6040bc5464b 100644 --- a/doc/handbook/ModelDescriptions/mpncimplicitmodel.tex +++ b/doc/handbook/ModelDescriptions/mpncimplicitmodel.tex @@ -6,7 +6,7 @@ This model implements a $M$-\/phase flow of a fluid mixture composed of $N$ chemical species. The phases are denoted by lower index $\alpha \in \{ 1, \dots, M \}$. All fluid phases are mixtures of $N \geq M - 1$ chemical species which are denoted by the upper index $\kappa \in \{ 1, \dots, N \} $. -The momentum approximation can be selected via \char`\"{}\-Base\-Flux\-Variables\char`\"{}\-: Darcy (\hyperlink{a00267}{Implicit\-Darcy\-Flux\-Variables}) and Forchheimer (\hyperlink{a00268}{Implicit\-Forchheimer\-Flux\-Variables}) relations are available for all Box models. +The momentum approximation can be selected via \char`\"{}\-Base\-Flux\-Variables\char`\"{}\-: Darcy (\hyperlink{a00270}{Implicit\-Darcy\-Flux\-Variables}) and Forchheimer (\hyperlink{a00271}{Implicit\-Forchheimer\-Flux\-Variables}) relations are available for all Box models. By inserting this into the equations for the conservation of the mass of each component, one gets one mass-\/continuity equation for each component $\kappa$ \[ \sum_{\kappa} \left( \phi \frac{\partial \left(\varrho_\alpha x_\alpha^\kappa S_\alpha\right)}{\partial t} + \mathrm{div}\; \left\{ v_\alpha \frac{\varrho_\alpha}{\overline M_\alpha} x_\alpha^\kappa \right\} \right) = q^\kappa \] with $\overline M_\alpha$ being the average molar mass of the phase $\alpha$\-: \[ \overline M_\alpha = \sum_\kappa M^\kappa \; x_\alpha^\kappa \] diff --git a/doc/handbook/ModelDescriptions/stokes2cimplicitmodel.tex b/doc/handbook/ModelDescriptions/stokesncimplicitmodel.tex similarity index 62% rename from doc/handbook/ModelDescriptions/stokes2cimplicitmodel.tex rename to doc/handbook/ModelDescriptions/stokesncimplicitmodel.tex index 5ffdf2893a5c783a21eb134c03c04d598af1740a..a7db0e0577ad80a87db76279a4a24b7a95e033fb 100644 --- a/doc/handbook/ModelDescriptions/stokes2cimplicitmodel.tex +++ b/doc/handbook/ModelDescriptions/stokesncimplicitmodel.tex @@ -4,13 +4,13 @@ % file instead!! % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -This model implements an isothermal two-\/component Stokes flow of a fluid solving a momentum balance, a mass balance and a conservation equation for one component. +This model implements an isothermal n-\/component Stokes flow of a fluid solving a momentum balance, a mass balance and a conservation equation for each component. When using mole fractions naturally the densities represent molar densites Momentum Balance\-: \[ \frac{\partial \left(\varrho_g {\boldsymbol{v}}_g\right)}{\partial t} + \boldsymbol{\nabla} \boldsymbol{\cdot} \left(p_g {\bf {I}} - \mu_g \left(\boldsymbol{\nabla} \boldsymbol{v}_g + \boldsymbol{\nabla} \boldsymbol{v}_g^T\right)\right) - \varrho_g {\bf g} = 0, \] Mass balance equation\-: \[ \frac{\partial \varrho_g}{\partial t} + \boldsymbol{\nabla}\boldsymbol{\cdot}\left(\varrho_g {\boldsymbol{v}}_g\right) - q_g = 0 \] -\hyperlink{a00085}{Component} mass balance equation\-: \[ \frac{\partial \left(\varrho_g X_g^\kappa\right)}{\partial t} + \boldsymbol{\nabla} \boldsymbol{\cdot} \left( \varrho_g {\boldsymbol{v}}_g X_g^\kappa - D^\kappa_g \varrho_g \frac{M^\kappa}{M_g} \boldsymbol{\nabla} x_g^\kappa \right) - q_g^\kappa = 0 \] +\hyperlink{a00084}{Component} mass balance equations\-: \[ \frac{\partial \left(\varrho_g X_g^\kappa\right)}{\partial t} + \boldsymbol{\nabla} \boldsymbol{\cdot} \left( \varrho_g {\boldsymbol{v}}_g X_g^\kappa - D^\kappa_g \varrho_g \boldsymbol{\nabla} X_g^\kappa \right) - q_g^\kappa = 0 \] -This is discretized using a fully-\/coupled vertex centered finite volume (box) scheme as spatial and the implicit Euler method as temporal discretization. +This is discretized using a fully-\/coupled vertex centered finite volume (box) scheme as spatial and the implicit Euler method in time. diff --git a/doc/handbook/ModelDescriptions/stokes2cniimplicitmodel.tex b/doc/handbook/ModelDescriptions/stokesncniimplicitmodel.tex similarity index 83% rename from doc/handbook/ModelDescriptions/stokes2cniimplicitmodel.tex rename to doc/handbook/ModelDescriptions/stokesncniimplicitmodel.tex index 7964642684c9109e09900e0c50004a7164259f7c..76c9321d171c985fa319cf12f2ff7918ca3611f1 100644 --- a/doc/handbook/ModelDescriptions/stokes2cniimplicitmodel.tex +++ b/doc/handbook/ModelDescriptions/stokesncniimplicitmodel.tex @@ -4,13 +4,13 @@ % file instead!! % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -This model implements a non-\/isothermal two-\/component Stokes flow of a fluid solving a momentum balance, a mass balance, a conservation equation for one component, and one balance equation for the energy. +This model implements a non-\/isothermal n-\/component Stokes flow of a fluid solving a momentum balance, a mass balance, a conservation equation for one component, and one balance equation for the energy. Momentum Balance\-: \[ \frac{\partial \left(\varrho_g {\boldsymbol{v}}_g\right)}{\partial t} + \boldsymbol{\nabla} \boldsymbol{\cdot} \left(p_g {\bf {I}} - \mu_g \left(\boldsymbol{\nabla} \boldsymbol{v}_g + \boldsymbol{\nabla} \boldsymbol{v}_g^T\right)\right) - \varrho_g {\bf g} = 0, \] Mass balance equation\-: \[ \frac{\partial \varrho_g}{\partial t} + \boldsymbol{\nabla}\boldsymbol{\cdot}\left(\varrho_g {\boldsymbol{v}}_g\right) - q_g = 0 \] -\hyperlink{a00085}{Component} mass balance equation\-: \[ \frac{\partial \left(\varrho_g X_g^\kappa\right)}{\partial t} + \boldsymbol{\nabla} \boldsymbol{\cdot} \left( \varrho_g {\boldsymbol{v}}_g X_g^\kappa - D^\kappa_g \varrho_g \frac{M^\kappa}{M_g} \boldsymbol{\nabla} x_g^\kappa \right) - q_g^\kappa = 0 \] +\hyperlink{a00084}{Component} mass balance equation\-: \[ \frac{\partial \left(\varrho_g X_g^\kappa\right)}{\partial t} + \boldsymbol{\nabla} \boldsymbol{\cdot} \left( \varrho_g {\boldsymbol{v}}_g X_g^\kappa - D^\kappa_g \varrho_g \frac{M^\kappa}{M_g} \boldsymbol{\nabla} x_g^\kappa \right) - q_g^\kappa = 0 \] Energy balance equation\-: \[ \frac{\partial (\varrho_g u_g)}{\partial t} + \boldsymbol{\nabla} \left( \boldsymbol{\cdot} \varrho_g h_g {\boldsymbol{v}}_g - \lambda_g \boldsymbol{\nabla} T \right) - q_T = 0 \] diff --git a/doc/handbook/models.tex b/doc/handbook/models.tex index 86b8d3b51d7601d10036a49b4d02bdd3575d9498..acd3d7b04d71d6d3e3ca8d9d53f0a0046819a792 100644 --- a/doc/handbook/models.tex +++ b/doc/handbook/models.tex @@ -252,11 +252,11 @@ subdirectories of \texttt{dumux/implicit} of the \Dumux distribution. \subsubsection{The Stokes model: StokesModel} \input{ModelDescriptions/stokesimplicitmodel} -\subsubsection{The isothermal two-component Stokes model: Stokes2cModel} -\input{ModelDescriptions/stokes2cimplicitmodel} +\subsubsection{The isothermal $N$-component Stokes model: StokesNcModel} +\input{ModelDescriptions/stokesncimplicitmodel} -\subsubsection{The non-isothermal two-component Stokes model: Stokes2cniModel} -\input{ModelDescriptions/stokes2cniimplicitmodel} +\subsubsection{The non-isothermal $N$-component Stokes model: StokesNcNIModel} +\input{ModelDescriptions/stokesncniimplicitmodel} \subsubsection{The linear elastic model: ElasticModel} \input{ModelDescriptions/elasticmodel}