From 18f9a7a8c788fcc4246e4337cf1dacc1aeebef03 Mon Sep 17 00:00:00 2001
From: Katharina Heck <katharina.heck@iws.uni-stuttgart.de>
Date: Thu, 29 Oct 2020 10:10:45 +0100
Subject: [PATCH] [docu][rans] update model descriptions
---
dumux/freeflow/rans/oneeq/model.hh | 12 ++++-----
dumux/freeflow/rans/twoeq/kepsilon/model.hh | 24 ++++++++---------
dumux/freeflow/rans/twoeq/komega/model.hh | 24 ++++++++---------
.../rans/twoeq/lowrekepsilon/model.hh | 26 +++++++++----------
4 files changed, 43 insertions(+), 43 deletions(-)
diff --git a/dumux/freeflow/rans/oneeq/model.hh b/dumux/freeflow/rans/oneeq/model.hh
index 97160c26a1..06e5f75e7f 100644
--- a/dumux/freeflow/rans/oneeq/model.hh
+++ b/dumux/freeflow/rans/oneeq/model.hh
@@ -36,12 +36,12 @@
* term which account for the transition or trip, is dropped from the original equations,
* such that the balance equation simplifies to:
* \f[
- * \frac{\partial \tilde{\nu}}{\partial t}
- * + \nabla \cdot \left( \tilde{\nu} \textbf{v} \right)
- * - c_\text{b1} \tilde{S} \tilde{\nu}
- * - \frac{1}{\sigma_{\tilde{\nu}}} \nabla \cdot \left( \left[ \nu + \tilde{\nu} \right] \nabla \tilde{\nu} \right)
- * - \frac{c_\text{b2}}{\sigma_{\tilde{\nu}}} \left| \nabla \tilde{\nu} \right|^2
- * + c_\text{w1} f_\text{w} \frac{\tilde{\nu}^2}{y^2}
+ * \frac{\partial \tilde{\nu}\varrho}{\partial t}
+ * + \nabla \cdot \left( \tilde{\nu} \varrho \textbf{v} \right)
+ * - c_\text{b1} \tilde{S} \tilde{\nu} \varrho
+ * - \frac{1}{\sigma_{\tilde{\nu}}} \nabla \cdot \left( \left[ \mu + \tilde{\nu} \varrho \right] \nabla \tilde{\nu} \right)
+ * - \frac{c_\text{b2}}{\sigma_{\tilde{\nu}}} \varrho \left| \nabla \tilde{\nu} \right|^2
+ * + c_\text{w1} f_\text{w} \varrho \frac{\tilde{\nu}^2}{y^2}
* = 0
* \f]
*
diff --git a/dumux/freeflow/rans/twoeq/kepsilon/model.hh b/dumux/freeflow/rans/twoeq/kepsilon/model.hh
index 6d87a2f9fc..e33a6720ae 100644
--- a/dumux/freeflow/rans/twoeq/kepsilon/model.hh
+++ b/dumux/freeflow/rans/twoeq/kepsilon/model.hh
@@ -31,27 +31,27 @@
*
* The turbulent kinetic energy balance is:
* \f[
- * \frac{\partial \left( k \right)}{\partial t}
- * + \nabla \cdot \left( \textbf{v} k \right)
- * - \nabla \cdot \left( \left( \nu + \frac{\nu_\text{t}}{\sigma_\text{k}} \right) \nabla k \right)
- * - 2 \nu_\text{t} \textbf{S} \cdot \textbf{S}
- * + \varepsilon
+ * \frac{\partial \left( \varrho k \right)}{\partial t}
+ * + \nabla \cdot \left( \textbf{v} \varhho k \right)
+ * - \nabla \cdot \left( \left( \mu + \frac{\mu_\text{t}}{\sigma_\text{k}} \right) \nabla k \right)
+ * - 2 \mu_\text{t} \textbf{S} \cdot \textbf{S}
+ * + \varrho \varepsilon
* = 0
* \f].
*
* The dissipation balance is:
* \f[
- * \frac{\partial \left( \varepsilon \right)}{\partial t}
- * + \nabla \cdot \left( \textbf{v} \varepsilon \right)
- * - \nabla \cdot \left( \left( \nu + \frac{\nu_\text{t}}{\sigma_{\varepsilon}} \right) \nabla \varepsilon \right)
- * - C_{1\varepsilon} \frac{\varepsilon}{k} 2 \nu_\text{t} \textbf{S} \cdot \textbf{S}
- * + C_{2\varepsilon} \frac{\varepsilon^2}{k}
+ * \frac{\partial \left( \varrho \varepsilon \right)}{\partial t}
+ * + \nabla \cdot \left( \textbf{v} \varrho \varepsilon \right)
+ * - \nabla \cdot \left( \left( \mu + \frac{\mu_\text{t}}{\sigma_{\varepsilon}} \right) \nabla \varepsilon \right)
+ * - C_{1\varepsilon} \frac{\varepsilon}{k} 2 \mu_\text{t} \textbf{S} \cdot \textbf{S}
+ * + C_{2\varepsilon} \varrho \frac{\varepsilon^2}{k}
* = 0
* \f].
*
- * The kinematic eddy viscosity \f$ \nu_\text{t} \f$ is:
+ * The dynamic eddy viscosity \f$ \mu_\text{t} \f$ is:
* \f[
- * \nu_\text{t} = C_\mu \frac{k^2}{\tilde{\varepsilon}}
+ * \mu_\text{t} = \varrho C_\mu \frac{k^2}{\tilde{\varepsilon}}
* \f].
*
* Finally, the model is closed with the following constants:
diff --git a/dumux/freeflow/rans/twoeq/komega/model.hh b/dumux/freeflow/rans/twoeq/komega/model.hh
index eb404167da..4c3e95b783 100644
--- a/dumux/freeflow/rans/twoeq/komega/model.hh
+++ b/dumux/freeflow/rans/twoeq/komega/model.hh
@@ -30,33 +30,33 @@
*
* 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]
+ * \frac{\partial \left( \varrho k \right)}{\partial t}
+ * + \nabla \cdot \left( \mathbf{v} \varrho k \right)
+ * - \nabla \cdot \left[ \left( \mu + \sigma_\textrm{k} \mu_\textrm{t} \right) \nabla k \right]
* - P
- * + \beta_k^{*} k \omega
+ * + \beta_k^{*} k \varrho \omega
* = 0
* \f]
- * with \f$ P = 2 \nu_\textrm{t} \mathbf{S} \cdot \mathbf{S} \f$
+ * with \f$ P = 2 \mu_\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$.
*
* Dissipation balance:
* \f[
- * \frac{\partial \left( \omega \right)}{\partial t}
- * + \nabla \cdot \left( \mathbf{v} \omega \right)
- * - \nabla \cdot \left[ \left( \nu + \sigma_{\omega} \nu_\textrm{t} \right) \nabla \omega \right]
+ * \frac{\partial \left( \varrho \omega \right)}{\partial t}
+ * + \nabla \cdot \left( \mathbf{v} \varrho \omega \right)
+ * - \nabla \cdot \left[ \left( \mu + \sigma_{\omega} \mu_\textrm{t} \right) \nabla \omega \right]
* - \alpha \frac{\omega}{k} P
* + \beta_{\omega} \omega^2
- * - \frac{\sigma_d}{\omega} \nabla k \nabla \omega
+ * - \varrho \frac{\sigma_d}{\omega} \nabla k \nabla \omega
* = 0
* \f]
*
- * The kinematic eddy viscosity \f$ \nu_\textrm{t} \f$ is calculated as follows:
- * \f[ \nu_\textrm{t} = \frac{k}{\tilde{\omega}} \f]
+ * The dynamic eddy viscosity \f$ \mu_\textrm{t} \f$ is calculated as follows:
+ * \f[ \mu_\textrm{t} = \varrho \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]
+ * \f[ \tilde{\omega} = \textrm{max} \left\{ \omega, 0.875 \sqrt{\frac{P}{\mu_\textrm{t} \beta_\textrm{k}}} \right\} \f]
*
* And a cross-diffusion coefficient \f$ \sigma_\textrm{d} \f$
* \f[
diff --git a/dumux/freeflow/rans/twoeq/lowrekepsilon/model.hh b/dumux/freeflow/rans/twoeq/lowrekepsilon/model.hh
index 79da934562..7365c59d80 100644
--- a/dumux/freeflow/rans/twoeq/lowrekepsilon/model.hh
+++ b/dumux/freeflow/rans/twoeq/lowrekepsilon/model.hh
@@ -34,30 +34,30 @@
* \f$ \varepsilon = \tilde{\varepsilon} + D_\varepsilon \f$:
*
* \f[
- * \frac{\partial \left( k \right)}{\partial t}
- * + \nabla \cdot \left( \textbf{v} k \right)
- * - \nabla \cdot \left( \left( \nu + \frac{\nu_\text{t}}{\sigma_\text{k}} \right) \nabla k \right)
- * - 2 \nu_\text{t} \textbf{S} \cdot \textbf{S}
- * + \tilde{\varepsilon}
- * + D_\varepsilon
+ * \frac{\partial \left( \varrho k \right)}{\partial t}
+ * + \nabla \cdot \left( \textbf{v} \varhho k \right)
+ * - \nabla \cdot \left( \left( \mu + \frac{\mu_\text{t}}{\sigma_\text{k}} \right) \nabla k \right)
+ * - 2 \mu_\text{t} \textbf{S} \cdot \textbf{S}
+ * + \varrho \tilde{\varepsilon}
+ * + D_\varepsilon \varrho
* = 0
* \f].
*
* The dissipation balance is changed by introducing additional functions
* (\f$ E_\text{k}\f$, \f$ f_1 \f$, and \f$ f_2 \f$) to account for a dampening towards the wall:
* \f[
- * \frac{\partial \left( \tilde{\varepsilon} \right)}{\partial t}
- * + \nabla \cdot \left( \textbf{v} \tilde{\varepsilon} \right)
- * - \nabla \cdot \left( \left( \nu + \frac{\nu_\text{t}}{\sigma_{\varepsilon}} \right) \nabla \tilde{\varepsilon} \right)
- * - C_{1\tilde{\varepsilon}} f_1 \frac{\tilde{\varepsilon}}{k} 2 \nu_\text{t} \textbf{S} \cdot \textbf{S}
- * + C_{2\tilde{\varepsilon}} f_2 \frac{\tilde{\varepsilon}^2}{k}
- * - E_\text{k}
+ * \frac{\partial \left( \varrho \tilde{\varepsilon} \right)}{\partial t}
+ * + \nabla \cdot \left( \textbf{v} \varrho \tilde{\varepsilon} \right)
+ * - \nabla \cdot \left( \left( \mu + \frac{\mu_\text{t}}{\sigma_{\varepsilon}} \right) \nabla \tilde{\varepsilon} \right)
+ * - C_{1\tilde{\varepsilon}} f_1 \frac{\tilde{\varepsilon}}{k} 2 \mu_\text{t} \textbf{S} \cdot \textbf{S}
+ * + C_{2\tilde{\varepsilon}} \varrho f_2 \frac{\tilde{\varepsilon}^2}{k}
+ * - E_\text{k} \varrho
* = 0
* \f].
*
* The kinematic eddy viscosity \f$ \nu_\text{t} \f$ is dampened by \f$ f_\mu \f$:
* \f[
- * \nu_\text{t} = C_\mu f_\mu \frac{k^2}{\tilde{\varepsilon}}
+ * \mu_\text{t} = \varrho C_\mu f_\mu \frac{k^2}{\tilde{\varepsilon}}
* \f].
*
* The auxiliary and dampening functions are defined as:
--
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