diff --git a/dumux/freeflow/stokes/stokesmodel.hh b/dumux/freeflow/stokes/stokesmodel.hh index 8a234eec7e2a162d033547d159ffabf7fca8c523..d9f36bfcfeb93a0b0fc2766a3ca0aee1e526208f 100644 --- a/dumux/freeflow/stokes/stokesmodel.hh +++ b/dumux/freeflow/stokes/stokesmodel.hh @@ -38,29 +38,29 @@ namespace Dumux { /*! * \ingroup BoxStokesModel - * \brief Adaption of the box scheme to the Stokes model. + * \brief Adaptation of the box scheme to the Stokes model. * * This model implements laminar Stokes flow of a single fluid, solving the momentum balance equation * \f[ -\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, + * \frac{\partial \left(\varrho_g {\boldsymbol{v}}_g\right)}{\partial t} + * + \text{div} \left( p_g {\bf {I}} + * - \mu_g \left( \textbf{grad}\, \boldsymbol{v}_g + * + \textbf{grad}\, \boldsymbol{v}_g^T \right) \right) + * - \varrho_g {\bf g} = 0 * \f] - * - * and the mass balance equation - * \f[ -\frac{\partial \varrho_g}{\partial t} + \boldsymbol{\nabla}\boldsymbol{\cdot}\left(\varrho_g {\boldsymbol{v}}_g\right) - q_g = 0. - * \f] - * * By setting the property <code>EnableNavierStokes</code> to <code>true</code> the Navier-Stokes * equation can be solved. In this case an additional term * \f[ - * + \varrho_g \left(\boldsymbol{v}_g \boldsymbol{\cdot} \boldsymbol{\nabla} \right) \boldsymbol{v}_g + * + \text{div} \left( \varrho_g \boldsymbol{v}_g \boldsymbol{v}_g \right) * \f] * is added to the momentum balance equation. * + * The mass balance equation: + * \f[ + * \frac{\partial \varrho_g}{\partial t} + * + \text{div} \left(\varrho_g {\boldsymbol{v}}_g\right) - q_g = 0 + * \f] + * * This is discretized by a fully-coupled vertex-centered finite volume * (box) scheme in space and by the implicit Euler method in time. */ diff --git a/dumux/freeflow/stokesnc/stokesncmodel.hh b/dumux/freeflow/stokesnc/stokesncmodel.hh index 9928e7c037e592654cda9f55aae3f0cf60e34d0e..1791dd0a332d8a15a5be49095c3980311c9f19db 100644 --- a/dumux/freeflow/stokesnc/stokesncmodel.hh +++ b/dumux/freeflow/stokesnc/stokesncmodel.hh @@ -34,38 +34,46 @@ namespace Dumux { /*! * \ingroup BoxStokesncModel - * \brief Adaptation of the BOX scheme to the compositional Stokes model. + * \brief Adaptation of the box scheme to the compositional Stokes model. * * 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 + * solving a momentum balance, a mass balance and conservation equations for \f$n-1\f$ + * components. When using mole fractions naturally the densities represent molar + * densities * - * Momentum Balance: + * The momentum balance: * \f[ -\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, + * \frac{\partial \left(\varrho_g {\boldsymbol{v}}_g\right)}{\partial t} + * + \text{div} \left( p_g {\bf {I}} + * - \mu_g \left( \textbf{grad}\, \boldsymbol{v}_g + * + \textbf{grad}\, \boldsymbol{v}_g^T \right) \right) + * - \varrho_g {\bf g} = 0 * \f] + * By setting the property <code>EnableNavierStokes</code> to <code>true</code> the Navier-Stokes + * equation can be solved. In this case an additional term + * \f[ + * + \text{div} \left( \varrho_g \boldsymbol{v}_g \boldsymbol{v}_g \right) + * \f] + * is added to the momentum balance equation. * - * Mass balance equation: + * The mass balance equation: * \f[ -\frac{\partial \varrho_g}{\partial t} + \boldsymbol{\nabla}\boldsymbol{\cdot}\left(\varrho_g {\boldsymbol{v}}_g\right) - q_g = 0 + * \frac{\partial \varrho_g}{\partial t} + * + \text{div} \left(\varrho_g {\boldsymbol{v}}_g\right) - q_g = 0 * \f] * - * Component mass balance equations: + * The component mass balance equations: * \f[ - \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 + * \frac{\partial \left(\varrho_g X_g^\kappa\right)}{\partial t} + * + \text{div} \left( \varrho_g {\boldsymbol{v}}_g X_g^\kappa + * - D^\kappa_g \varrho_g \frac{M^\kappa}{M_g} \textbf{grad}\, x_g^\kappa \right) + * - q_g^\kappa = 0 * \f] + * Please note that, even though it is n-component model, the diffusive + * fluxes are still calculated with binary diffusion. * - * This is discretized using a fully-coupled vertex - * centered finite volume (box) scheme as spatial and - * the implicit Euler method in time. + * This is discretized by a fully-coupled vertex-centered finite volume + * (box) scheme in space and by the implicit Euler method in time. */ template<class TypeTag> class StokesncModel : public StokesModel<TypeTag> diff --git a/dumux/freeflow/stokesncni/stokesncnimodel.hh b/dumux/freeflow/stokesncni/stokesncnimodel.hh index 323c9b1a007774c0a255f46cb327f2f6e81e9fba..b12f9d34a7341765cca4b5d8ad22fa030862637c 100644 --- a/dumux/freeflow/stokesncni/stokesncnimodel.hh +++ b/dumux/freeflow/stokesncni/stokesncnimodel.hh @@ -19,8 +19,8 @@ /*! * \file * - * \brief Adaption of the BOX scheme to the non-isothermal - * compositional stokes model (with n components). + * \brief Adaptation of the box scheme to the non-isothermal + * n-component Stokes model. */ #ifndef DUMUX_STOKESNCNI_MODEL_HH #define DUMUX_STOKESNCNI_MODEL_HH @@ -35,46 +35,55 @@ namespace Dumux { /*! * \ingroup BoxStokesncniModel - * \brief Adaption of the BOX scheme to the non-isothermal compositional n-component Stokes model. + * \brief Adaptation of the box scheme to the non-isothermal + * n-component Stokes model. * * 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, + * solving a momentum balance, a mass balance, conservation equations for \f$n-1\f$ components, * and one balance equation for the energy. * - * Momentum Balance: + * The momentum balance: * \f[ -\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, + * \frac{\partial \left(\varrho_g {\boldsymbol{v}}_g\right)}{\partial t} + * + \text{div} \left( p_g {\bf {I}} + * - \mu_g \left( \textbf{grad}\, \boldsymbol{v}_g + * + \textbf{grad}\, \boldsymbol{v}_g^T \right) \right) + * - \varrho_g {\bf g} = 0 * \f] - * - * Mass balance equation: + * By setting the property <code>EnableNavierStokes</code> to <code>true</code> the Navier-Stokes + * equation can be solved. In this case an additional term * \f[ -\frac{\partial \varrho_g}{\partial t} + \boldsymbol{\nabla}\boldsymbol{\cdot}\left(\varrho_g {\boldsymbol{v}}_g\right) - q_g = 0 + * + \text{div} \left( \varrho_g \boldsymbol{v}_g \boldsymbol{v}_g \right) * \f] + * is added to the momentum balance equation. * - * Component mass balance equation: + * The mass balance equation: * \f[ - \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 + * \frac{\partial \varrho_g}{\partial t} + * + \text{div} \left(\varrho_g {\boldsymbol{v}}_g\right) - q_g = 0 * \f] * - * Energy balance equation: + * The component mass balance equations: * \f[ -\frac{\partial (\varrho_g u_g)}{\partial t} -+ \boldsymbol{\nabla} \boldsymbol{\cdot} \left( \varrho_g h_g {\boldsymbol{v}}_g -- \sum_\kappa \left[ h^\kappa_g D^\kappa_g \varrho_g \frac{M^\kappa}{M_g} \nabla x^\kappa_g \right] -- \lambda_g \boldsymbol{\nabla} T \right) - q_T = 0 + * \frac{\partial \left(\varrho_g X_g^\kappa\right)}{\partial t} + * + \text{div} \left( \varrho_g {\boldsymbol{v}}_g X_g^\kappa + * - D^\kappa_g \varrho_g \frac{M^\kappa}{M_g} \textbf{grad}\, x_g^\kappa \right) + * - q_g^\kappa = 0 * \f] + * Please note that, even though it is n-component model, the diffusive + * fluxes are still calculated with binary diffusion. * - * This is discretized using a fully-coupled vertex - * centered finite volume (box) scheme as spatial and - * the implicit Euler method as temporal discretization. + * The energy balance equation: + * \f[ + * \frac{\partial (\varrho_g u_g)}{\partial t} + * + \text{div} \left( \varrho_g h_g {\boldsymbol{v}}_g + * - \sum_\kappa \left[ h^\kappa_g D^\kappa_g \varrho_g \frac{M^\kappa}{M_g} + * \textbf{grad}\, x^\kappa_g \right] + * - \lambda_g \textbf{grad}\, T \right) - q_T = 0 + * \f] * + * This is discretized by a fully-coupled vertex-centered finite volume + * (box) scheme in space and by the implicit Euler method in time. */ template<class TypeTag> class StokesncniModel : public StokesncModel<TypeTag> diff --git a/dumux/freeflow/zeroeq/zeroeqmodel.hh b/dumux/freeflow/zeroeq/zeroeqmodel.hh index dcccae55209f3f0ac470b9ad995e532d7518aab4..f65750fbc4b83da959c779aa5fa4902f425a9c67 100644 --- a/dumux/freeflow/zeroeq/zeroeqmodel.hh +++ b/dumux/freeflow/zeroeq/zeroeqmodel.hh @@ -43,21 +43,21 @@ namespace Dumux * Mass balance: * \f[ * \frac{\partial \varrho_\textrm{g}}{\partial t} - * + \boldsymbol{\nabla}\boldsymbol{\cdot}\left(\varrho_\textrm{g} {\boldsymbol{v}}_\textrm{g}\right) + * + \text{div} \left( \varrho_\textrm{g} {\boldsymbol{v}}_\textrm{g} \right) * - q_\textrm{g} = 0 * \f] * * Momentum Balance: * \f[ * \frac{\partial \left(\varrho_\textrm{g} {\boldsymbol{v}}_\textrm{g}\right)}{\partial t} - * + \boldsymbol{\nabla} \boldsymbol{\cdot} \left( + * + \text{div} \left( * \varrho_\textrm{g} {\boldsymbol{v}_\textrm{g} {\boldsymbol{v}}_\textrm{g}} * - \left[ \mu_\textrm{g} + \mu_\textrm{g,t} \right] - * \left(\boldsymbol{\nabla} \boldsymbol{v}_\textrm{g} - * + \boldsymbol{\nabla} \boldsymbol{v}_\textrm{g}^T \right) + * \left( \textbf{grad}\, \boldsymbol{v}_\textrm{g} + * + \textbf{grad}\, \boldsymbol{v}_\textrm{g}^T \right) * \right) * + \left(p_\textrm{g} {\bf {I}} \right) - * - \varrho_\textrm{g} {\bf g} = 0, + * - \varrho_\textrm{g} {\bf g} = 0 * \f] * * This is discretized by a fully-coupled vertex-centered finite volume diff --git a/dumux/freeflow/zeroeqnc/zeroeqncmodel.hh b/dumux/freeflow/zeroeqnc/zeroeqncmodel.hh index 199ca9f169b3bd80b2e7807b6aedf1af1d68064e..3c089ee4819a6dcf2bec85f9d0b42564c5584de4 100644 --- a/dumux/freeflow/zeroeqnc/zeroeqncmodel.hh +++ b/dumux/freeflow/zeroeqnc/zeroeqncmodel.hh @@ -42,31 +42,33 @@ namespace Dumux * Mass balance: * \f[ * \frac{\partial \varrho_\textrm{g}}{\partial t} - * + \boldsymbol{\nabla}\boldsymbol{\cdot}\left(\varrho_\textrm{g} {\boldsymbol{v}}_\textrm{g}\right) + * + \text{div} \left( \varrho_\textrm{g} {\boldsymbol{v}}_\textrm{g} \right) * - q_\textrm{g} = 0 * \f] * * Momentum Balance: * \f[ * \frac{\partial \left(\varrho_\textrm{g} {\boldsymbol{v}}_\textrm{g}\right)}{\partial t} - * + \boldsymbol{\nabla} \boldsymbol{\cdot} \left( + * + \text{div} \left( * \varrho_\textrm{g} {\boldsymbol{v}_\textrm{g} {\boldsymbol{v}}_\textrm{g}} * - \left[ \mu_\textrm{g} + \mu_\textrm{g,t} \right] - * \left(\boldsymbol{\nabla} \boldsymbol{v}_\textrm{g} - * + \boldsymbol{\nabla} \boldsymbol{v}_\textrm{g}^T \right) + * \left( \textbf{grad}\, \boldsymbol{v}_\textrm{g} + * + \textbf{grad}\, \boldsymbol{v}_\textrm{g}^T \right) * \right) * + \left(p_\textrm{g} {\bf {I}} \right) - * - \varrho_\textrm{g} {\bf g} = 0, + * - \varrho_\textrm{g} {\bf g} = 0 * \f] * * Component mass balance equations: * \f[ * \frac{\partial \left(\varrho_\textrm{g} X_\textrm{g}^\kappa\right)}{\partial t} - * + \boldsymbol{\nabla} \boldsymbol{\cdot} \left( \varrho_\textrm{g} {\boldsymbol{v}}_\textrm{g} X_\textrm{g}^\kappa + * + \text{div} \left( \varrho_\textrm{g} {\boldsymbol{v}}_\textrm{g} X_\textrm{g}^\kappa * - \left[ D^\kappa_\textrm{g} + D^\kappa_\textrm{g,t} \right] - * \varrho_\textrm{g} \frac{M^\kappa}{M_\textrm{g}} \boldsymbol{\nabla} x_\textrm{g}^\kappa \right) + * \varrho_\textrm{g} \frac{M^\kappa}{M_\textrm{g}} \textbf{grad}\, x_\textrm{g}^\kappa \right) * - q_\textrm{g}^\kappa = 0 * \f] + * Please note that, even though it is n-component model, the diffusive + * fluxes are still calculated with binary diffusion. * * This is discretized by a fully-coupled vertex-centered finite volume * (box) scheme in space and by the implicit Euler method in time. diff --git a/dumux/freeflow/zeroeqncni/zeroeqncnimodel.hh b/dumux/freeflow/zeroeqncni/zeroeqncnimodel.hh index 5ae50be080218a1df1479286f29ea15cedabc0fe..b5a53fba617e4af898adc03818204b0fbc59cdda 100644 --- a/dumux/freeflow/zeroeqncni/zeroeqncnimodel.hh +++ b/dumux/freeflow/zeroeqncni/zeroeqncnimodel.hh @@ -43,41 +43,43 @@ namespace Dumux * Mass balance: * \f[ * \frac{\partial \varrho_\textrm{g}}{\partial t} - * + \boldsymbol{\nabla}\boldsymbol{\cdot}\left(\varrho_\textrm{g} {\boldsymbol{v}}_\textrm{g}\right) + * + \text{div} \left( \varrho_\textrm{g} {\boldsymbol{v}}_\textrm{g} \right) * - q_\textrm{g} = 0 * \f] * * Momentum Balance: * \f[ * \frac{\partial \left(\varrho_\textrm{g} {\boldsymbol{v}}_\textrm{g}\right)}{\partial t} - * + \boldsymbol{\nabla} \boldsymbol{\cdot} \left( + * + \text{div} \left( * \varrho_\textrm{g} {\boldsymbol{v}_\textrm{g} {\boldsymbol{v}}_\textrm{g}} * - \left[ \mu_\textrm{g} + \mu_\textrm{g,t} \right] - * \left(\boldsymbol{\nabla} \boldsymbol{v}_\textrm{g} - * + \boldsymbol{\nabla} \boldsymbol{v}_\textrm{g}^T \right) + * \left( \textbf{grad}\, \boldsymbol{v}_\textrm{g} + * + \textbf{grad}\, \boldsymbol{v}_\textrm{g}^T \right) * \right) * + \left(p_\textrm{g} {\bf {I}} \right) - * - \varrho_\textrm{g} {\bf g} = 0, + * - \varrho_\textrm{g} {\bf g} = 0 * \f] * * Component mass balance equations: * \f[ * \frac{\partial \left(\varrho_\textrm{g} X_\textrm{g}^\kappa\right)}{\partial t} - * + \boldsymbol{\nabla} \boldsymbol{\cdot} \left( \varrho_\textrm{g} {\boldsymbol{v}}_\textrm{g} X_\textrm{g}^\kappa + * + \text{div} \left( \varrho_\textrm{g} {\boldsymbol{v}}_\textrm{g} X_\textrm{g}^\kappa * - \left[ D^\kappa_\textrm{g} + D^\kappa_\textrm{g,t} \right] - * \varrho_\textrm{g} \frac{M^\kappa}{M_\textrm{g}} \boldsymbol{\nabla} x_\textrm{g}^\kappa \right) + * \varrho_\textrm{g} \frac{M^\kappa}{M_\textrm{g}} \textbf{grad}\, x_\textrm{g}^\kappa \right) * - q_\textrm{g}^\kappa = 0 * \f] * * Energy balance equation: * \f[ * \frac{\partial (\varrho_\textrm{g} u_\textrm{g})}{\partial t} - * + \boldsymbol{\nabla} \boldsymbol{\cdot} \left( \varrho_\textrm{g} h_\textrm{g} {\boldsymbol{v}}_\textrm{g} + * + \text{div} \left( \varrho_\textrm{g} h_\textrm{g} {\boldsymbol{v}}_\textrm{g} * - \sum_\kappa \left( h^\kappa_\textrm{g} \left[ D^\kappa_\textrm{g} + D^\kappa_\textrm{g,t} \right] - * \varrho_\textrm{g} \frac{M^\kappa}{M_\textrm{g}} \nabla x^\kappa_\textrm{g} \right) - * - \left[ \lambda_\textrm{g} + \lambda_\textrm{g,t} \right] \boldsymbol{\nabla} T \right) + * \varrho_\textrm{g} \frac{M^\kappa}{M_\textrm{g}} \textbf{grad}\, x^\kappa_\textrm{g} \right) + * - \left[ \lambda_\textrm{g} + \lambda_\textrm{g,t} \right] \textbf{grad}\, T \right) * - q_\textrm{T} = 0 * \f] + * Please note that, even though it is n-component model, the diffusive + * fluxes are still calculated with binary diffusion. * * This is discretized by a fully-coupled vertex-centered finite volume * (box) scheme in space and by the implicit Euler method in time. diff --git a/dumux/material/binarycoefficients/h2o_air.hh b/dumux/material/binarycoefficients/h2o_air.hh index 4e9f77ff6c7eafaaa05c192629c71e4ea9391311..63ea8f4300c0e2a98d6aae0fc261af56d4139d8e 100644 --- a/dumux/material/binarycoefficients/h2o_air.hh +++ b/dumux/material/binarycoefficients/h2o_air.hh @@ -38,10 +38,10 @@ class H2O_Air { public: /*! - * \brief Henry coefficent \f$\mathrm{[N/m^2]}\f$ for air in liquid water. + * \brief Henry coefficient \f$\mathrm{[N/m^2]}\f$ for air in liquid water. * \param temperature the temperature \f$\mathrm{[K]}\f$ * - * Henry coefficent See: + * Henry coefficient See: * Stefan Finsterle, 1993 * Inverse Modellierung zur Bestimmung hydrogeologischer Parameter eines Zweiphasensystems * page 29 Formula (2.9) (nach Tchobanoglous & Schroeder, 1985) @@ -56,11 +56,12 @@ public: } /*! - * \brief Binary diffusion coefficent \f$\mathrm{[m^2/s]}\f$ for molecular water and air + * \brief Binary diffusion coefficient \f$\mathrm{[m^2/s]}\f$ for molecular water and air * * \param temperature the temperature \f$\mathrm{[K]}\f$ * \param pressure the phase pressure \f$\mathrm{[Pa]}\f$ - * Vargaftik : Tables on the thermophysical properties of liquids and gases. John Wiley & * Sons, New York, 1975. + * Vargaftik: Tables on the thermophysical properties of liquids and gases. + * John Wiley & Sons, New York, 1975. * * Walker, Sabey, Hampton: Studies of heat transfer and water migration in soils. * Dep. of Agricultural and Chemical Engineering, Colorado State University, @@ -83,7 +84,7 @@ public: /*! * Lacking better data on water-air diffusion in liquids, we use at the * moment the diffusion coefficient of the air's main component nitrogen!! - * \brief Diffusion coefficent \f$\mathrm{[m^2/s]}\f$ for molecular nitrogen in liquid water. + * \brief Diffusion coefficient \f$\mathrm{[m^2/s]}\f$ for molecular nitrogen in liquid water. * * \param temperature the temperature \f$\mathrm{[K]}\f$ * \param pressure the phase pressure \f$\mathrm{[Pa]}\f$ @@ -99,7 +100,7 @@ public: * R. Reid et al.: "The properties of Gases and Liquids", 4th edition, * pp. 599, McGraw-Hill, 1987 * - * R. Ferrell, D. Himmelblau: "Diffusion Coeffients of Nitrogen and + * R. Ferrell, D. Himmelblau: "Diffusion Coefficients of Nitrogen and * Oxygen in Water", Journal of Chemical Engineering and Data, * Vol. 12, No. 1, pp. 111-115, 1967 */