Hello everyone,
I have a question about the scalar diffusion coefficient set in the GUI under:
Volume conditions > all_cells > Diffusion coefficient of species.
For a bit of context i am talking about an atmospheric simulation where i define a user scalar to transport with the SGDH flux model (since i am using a k-epsilon turbulence model).
According to the theory guide p.18, the genearl scalar transport equation is :
\frac{\partial (\rho a)}{\partial t}
+ {\nabla \cdot (\rho a \mathbf{u})}
- {\nabla \cdot (K \nabla a)}
= S_{T_a} + \Gamma a_{\text{in}}
\label{eq:scalar_transport}
And the SGDH detail p.80 gives :
\rho \frac{da}{dt} = \nabla \cdot \left[ \left( \frac{\mu}{\text{Sc}} + \frac{\mu_T}{\text{Sc}_T} \right) \nabla a \right]
\label{eq:gradient_diffusion}
I arrived to the conclusion that the general formula for a scalar transport with the SGDH model is (and correct me if i’m wrong) :
\frac{\partial (\rho a)}{\partial t} + \nabla \cdot (\rho a \mathbf{u}) - \nabla \cdot \left( \left( \frac{\mu}{\text{Sc}} + \frac{\mu_T}{\text{Sc}T} \right) \nabla a \right) = S{T_a} + \Gamma a_{\text{in}}
\label{eq:full_scalar_transport}
But at this point i’m not sure where the scalar difusion coefficient is used. My best guess would be that it defines the \frac{\mu}{\text{Sc}} part of the equation (the molecular diffusion part) with the following relation : D =\frac{\mu}{\rho . \text{Sc}} .
And i also assume the turbulent part \frac{\mu_T}{\text{Sc}_T} is handled automatically by the SGDH model using μT from the k-ε model
Am i guessing wrong or not ? Thanks for your help.
Regards,
Cyril