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Update documentation for Solver Setup #81

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@suargi suargi commented Jun 28, 2022

Update the documentation of Solver-Setup.md

The idea is to make divide #59 into small pull requests in order to make things smoother and easier. This one addresses only the Solver-Setup.md.

There is documentation for certain fields still missing, e.g., SST_OPTIONS. I am not sure about each of them. I will work on that. Done.

There seems to be some problem with markdown-latex that I cannot solve. I will work on that. Something is odd. In my local machine everything works fine.

@suargi suargi mentioned this pull request Jun 28, 2022
@suargi suargi changed the title [WIP] Update documentation for Solver Setup Update documentation for Solver Setup Jun 29, 2022
The DES constant can be controlledd by the field `DES_CONST`, with 0.65 as default.

#### Menter’s k-omega SST Model ####
As initial conditions, the values of are initialized at all grid point with the farfield values. The farfield conditions for the turbulent kinetic energy $k$ is computed as: $k = \frac{3}{2}(UI)$, whereby $U$ is the freestream velocity magnitude and $I$ is the turbulence intensity. This latter value can be specified in the config file by the `FREESTREAM_TURBULENCEINTENSITY` field, with defaul value to 0.05 which corresponds to a $5\%$. The freestream value of the turbulent frequency $\omega$ is computed as: $\omega = \frac{\rho k}{\mu}(\frac{\mu_t}{\mu})^{-1}$, where $\rho$ and $\mu$ are the freestream density and laminar viscosity respectively and $\frac{\mu_t}{\mu}$ is the turbulent viscosity ratio, also known as freestream dissipation. Its value can be specified in the `FREESTREAM_TURB2LAMVISCRATIO` field, defaulting to $10$.
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Would be nice if someone checks the boundary conditions for omega. I am not that familiar with the k-w model.

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Comment on lines +60 to +70
- `SST_OPTIONS`:
- `NONE`: No SST turbulence model (default).
- `V1994m`: refers to the "Standard" Menter SST model from 1994 with the modified constant $\sigma_{k1}$ and the redefinition of the turbulent eddy viscosity.
- `V2003m`: refers to the Menter SST model from 2003 ignoring the $\tau_{ij}$ in the momentum and energy equations and the production term is approximated by $P = \mu_t S^2$.
- `VORTICITY`: refers to the vorticity source term correction.
- `KATO_LAUNDER`: refers to the Kato-Launder correction.
- `UQ`: refers to the V1994m version with uncertainty quantification modifications.??
- `SUSTAINING`: refers to the controlled decay correction.

- `SA_OPTIONS`:
- `NONE`: refers to the modification where the $f_{t2}$ term is set to zero, i.e., $c_{t3} = 0$ (default).
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This does not have to be repeated here... just point to the section in Physical definition.

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