diff --git a/doc/doxygen/modules.txt b/doc/doxygen/modules.txt index 3958a6f442b9083c1cd0aef39e4a598c4776e3ab..0b8619b1ac7ff2fed66de3479474d1a454a1ad25 100644 --- a/doc/doxygen/modules.txt +++ b/doc/doxygen/modules.txt @@ -202,6 +202,12 @@ * \brief K-epsilon model * \copydetails ./freeflow/rans/twoeq/kepsilon/model.hh */ + /*! + * \ingroup TwoEqModel + * \defgroup KOmegaModel K-omega model + * \brief K-omega model + * \copydetails ./freeflow/rans/twoeq/komega/model.hh + */ /*! * \ingroup TwoEqModel * \defgroup LowReKEpsilonModel Low-Re k-epsilon model diff --git a/doc/handbook/dumux-handbook.bib b/doc/handbook/dumux-handbook.bib index 6264fca6b7945e4453db6063e045660d1f9691df..4bfc36d0e30c0cceb43b464df2b4b2d909ff3b25 100644 --- a/doc/handbook/dumux-handbook.bib +++ b/doc/handbook/dumux-handbook.bib @@ -1702,3 +1702,15 @@ url={http://dx.doi.org/10.1007/s11242-015-0599-1} doi = {10.1016/j.physa.2005.09.006}, url = {https://doi.org/10.1016/j.physa.2005.09.006} } + +@Article{Wilcox2008a, + author = {David C. Wilcox}, + title = {{Formulation of the $k$-$\omega$ Turbulence Model Revisited}}, + journal = {AIAA Journal}, + year = {2008}, + volume = {46}, + pages = {2823--2838}, + number = {11}, + doi = {10.2514/1.36541}, + url = {https://doi.org/10.2514/1.36541} +} diff --git a/dumux/freeflow/rans/twoeq/komega/localresidual.hh b/dumux/freeflow/rans/twoeq/komega/localresidual.hh index 61764cc545a88c8457d0f082ff344d5e929280bc..d76f45c2b7f1b7c062c00f6e26fa8890e216bec5 100644 --- a/dumux/freeflow/rans/twoeq/komega/localresidual.hh +++ b/dumux/freeflow/rans/twoeq/komega/localresidual.hh @@ -18,8 +18,8 @@ *****************************************************************************/ /*! * \file - * \ingroup KOmega TwoEq Model - * \copydoc Dumux::KOmegaKOmegaResidual + * \ingroup KOmegaModel + * \copydoc Dumux::KOmegaResidual */ #ifndef DUMUX_KOMEGA_LOCAL_RESIDUAL_HH #define DUMUX_KOMEGA_LOCAL_RESIDUAL_HH @@ -37,7 +37,7 @@ template<class TypeTag, DiscretizationMethod discMethod> class KOmegaResidualImpl; /*! - * \ingroup KOmega TwoEq Model + * \ingroup KOmegaModel * \brief The local residual class for the k-omega model. This is a convenience alias for the actual, discretization-specific local residual. diff --git a/dumux/freeflow/rans/twoeq/komega/model.hh b/dumux/freeflow/rans/twoeq/komega/model.hh index 0a0dd92dae6e4b3054c65b02c94a52fd2701eb5b..f541c2ab280f5fd491aaa36ee1a67a97338f5c6e 100644 --- a/dumux/freeflow/rans/twoeq/komega/model.hh +++ b/dumux/freeflow/rans/twoeq/komega/model.hh @@ -24,8 +24,48 @@ * * \copydoc RANSModel * - * These models calculate the eddy viscosity with two additional PDEs, - * one for the turbulentKineticEnergy (k) and a second for the dissipation (omega). + * Two additional PDEs, one for the turbulentKineticEnergy (k) and a second for the dissipation (omega) + * are used to calculate the eddy viscosity for this model. + * The model is taken from Wilcox, 2008 \cite Wilcox2008a. + * + * Turbulent Kinetic Energy balance: + * \f[ + * \frac{\partial \left( k \right)}{\partial t} + * + \nabla \cdot \left( \mathbf{v} k \right) + * - \nabla \cdot \left[ \left( \nu + \sigma_\textrm{k} \nu_\textrm{t} \right) \nabla k \right] + * - P + * + \beta_k^{*} k \omega + * = 0 + * \f] + * with \f$ P = 2 \nu_\textrm{t} \mathbf{S} \cdot \mathbf{S} \f$ + * and \f$ S_{ij} = \frac{1}{2} \left[ \frac{\partial}{\partial x_i} v_j + \frac{\partial}{\partial x_j} v_i \right] \f$ + * based on \f$ a_{ij} \cdot b_{ij} = \sum_{i,j} a_{ij} b_{ij} \f$. + * + * Dissipation balance: + * \f[ + * \frac{\partial \left( \omega \right)}{\partial t} + * + \nabla \cdot \left( \mathbf{v} \omega \right) + * - \nabla \cdot \left[ \left( \nu + \sigma_{\omega} \nu_\textrm{t} \right) \nabla \omega \right] + * - \alpha \frac{\omega}{k} P + * + \beta_{\omega} \omega^2 + * - \frac{\sigma_d}{\omega} \nabla k \nabla \omega + * = 0 + * \f] + * + * The kinematic eddy viscosity \f$ \nu_\textrm{t} \f$ is calculated as follows: + * \f[ \nu_\textrm{t} = \frac{k}{\tilde{\omega}} \f] + * + * With a limited dissipation: + * \f[ \tilde{\omega} = \textrm{max} \left\{ \omega, 0.875 \sqrt{\frac{P}{\nu_\textrm{t} \beta_\textrm{k}}} \right\} \f] + * + * And a cross-diffusion coefficient \f$ \sigma_\textrm{d} \f$ + * \f[ + * \sigma_\text{d} = + * \begin{cases} + * 0 & \mbox{, if } \; \nabla k \cdot \nabla \omega \le 0 \\ + * 0.125 & \mbox{, if } \; \nabla k \cdot \nabla \omega > 0 + * \end{cases}. + * \f] */ #ifndef DUMUX_KOMEGA_MODEL_HH diff --git a/dumux/freeflow/rans/twoeq/komega/problem.hh b/dumux/freeflow/rans/twoeq/komega/problem.hh index fac8fd1a526d37bd6425089cefad106e5c9a0b4b..f7b1651447284852e14d3e46f23735649b91a596 100644 --- a/dumux/freeflow/rans/twoeq/komega/problem.hh +++ b/dumux/freeflow/rans/twoeq/komega/problem.hh @@ -18,8 +18,8 @@ *****************************************************************************/ /*! * \file - * \ingroup KOmega TwoEq Model - * \copydoc Dumux::KomegaProblem + * \ingroup KOmegaModel + * \copydoc Dumux::KOmegaProblem */ #ifndef DUMUX_KOMEGA_PROBLEM_HH #define DUMUX_KOMEGA_PROBLEM_HH @@ -37,7 +37,7 @@ namespace Dumux { /*! - * \ingroup KOmega TwoEq Model + * \ingroup KOmegaModel * \brief K-Omega turbulence model problem base class. * * This implements the 2-equation k-omega turbulence model developed in Wilcox08 and Wilcox88