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35 changes: 35 additions & 0 deletions _sources/source/theory/supportedEquationSet.rst.txt
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Expand Up @@ -855,6 +855,41 @@ where :math:`\Omega` is the earth's angular velocity and :math:`\lambda` is the

.. _eqn_sst_des:

Laminar-Turbulent Transition Model Formulation
++++++++++++++++++++++++++++++++++++++++++++++
To account for the effects of the laminar-turbulent boundary layer transition,
Menter's one-equation :math:`\gamma` transition model :cite:`Menter:2015` is coupled with the SST model.
The model consists of single transport equation for intermittency

.. math::
\frac{D(\rho \gamma)}{Dt}=P_{\gamma}-D_{\gamma}+\frac{\partial }{\partial x_j}\left[ (\mu + \frac{\mu_t}{\sigma_{\gamma}} )\frac{\partial \gamma}{\partial x_j} \right]
The production term, :math:`P_{\gamma}`, and destruction term, :math:`D_{\gamma}`, are as:

.. math::
P_{\gamma}=F_{length} \rho S \gamma (1-\gamma) F_{onset}, \quad D_{\gamma}=C_{a2} \rho \Omega \gamma F_{turb} (C_{e2}\gamma-1)
The model constants are:

.. math::
F_{length}=100, \quad c_{e2}=50, \quad c_{a2}=0.06, \quad \sigma_{\gamma}=1.0
The transition onset criteria of the model are defined as:

.. math::
F_{onset1}=\frac{Re_{v}}{2.2Re_{\theta c}}, \quad F_{onset2}=(F_{onset1},2.0 )
.. math::
F_{onset3}=\max \left(1- \left (\frac{R_{T}}{3.5}\right)^3,0 \right ), \quad F_{onset}=\max(F_{onset2}-F_{onset3},0)
.. math::
F_{turb}=e^{-\left ( \frac{R_{T}}{2} \right )^{4}}, \quad R_T=\frac{\rho k}{\mu \omega}, \quad Re_v=\frac{\rho d_{w}^2S}{\mu}
The transition onset occurs once the scaled vorticity Reynolds number, :math:`Re_{v}/2.2`, exceeds the critical momentum thickness Reynolds number, :math:`Re_{\theta c}`, from the empirical correlations.

The output intermittency from the transition model is applied to both the production and destruction terms of the turbulent kinetic energy
transport equation.

Detached Eddy Simulation (DES) Formulation
++++++++++++++++++++++++++++++++++++++++++

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110 changes: 110 additions & 0 deletions api_docs/_s_d_r_s_s_t_b_l_t_m2015_node_kernel_8_c.html
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<div class="textblock"><code>#include &quot;node_kernels/SDRSSTBLTM2015NodeKernel.h&quot;</code><br />
<code>#include &quot;Realm.h&quot;</code><br />
<code>#include &quot;SolutionOptions.h&quot;</code><br />
<code>#include &quot;SimdInterface.h&quot;</code><br />
<code>#include &quot;utils/StkHelpers.h&quot;</code><br />
<code>#include &quot;stk_mesh/base/MetaData.hpp&quot;</code><br />
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