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---
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title: Physical Definition and Non-dimensionalization
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title: Physical Definition
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permalink: /docs/Physical-Definition/
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---
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## Reference Values ##
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| Solver | Version |
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| --- | --- |
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| `EULER`, `NAVIER_STOKES`, `RANS`, `INC_EULER`, `INC_NAVIER_STOKES`, `INC_RANS`, `FEM_EULER`, `FEM_NAVIER_STOKES` | 7.0.0 |
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| Variable | Unit | Reference |
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|---|---|---|
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| Length | $$m$$ | $$l_{ref} = 1$$ |
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| Density | $$\frac{kg}{m^3}$$ | $$\rho_{ref}$$ (user input) |
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| Velocity | $$\frac{m}{s}$$ | $$v_{ref}$$ (user input)|
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| Temperature | $$K$$ | $$T_{ref}$$ (user input) |
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| Pressure | $$Pa$$ | $$p_{ref}$$ (user input) |
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| **Density** | $$\frac{kg}{m^3}$$ | $$\rho_{ref}$$ (based on user input) |
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| **Velocity** | $$\frac{m}{s}$$ | $$v_{ref}$$ (based on user input)|
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| **Temperature** | $$K$$ | $$T_{ref}$$ (based on user input) |
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| **Pressure** | $$Pa$$ | $$p_{ref}$$ (based on user input) |
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| Viscosity | $$\frac{kg}{ms}$$ | $$\mu_{ref} = \rho_{ref}v_{ref}l_{ref}$$ |
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| Time | $$s$$ | $$t_{ref} = \frac{l_{ref}}{v_{ref}}$$ |
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| Heatflux | $$\frac{W}{m^2}$$ | $$Q_{ref} = \rho_{ref}v^3_{ref} $$ |
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| Gas Constant | $$\frac{m^2}{s^2 K}$$ | $$R_{ref} = \frac{v^2_{ref}}{T_{ref}}$$|
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| Conductivity | $$\frac{W}{mK}$$ | $$k_{ref} = \mu_{ref}R_{ref}$$ |
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| Force | $$N$$ | $$ F_{ref} = \rho_{ref}v^2_{ref}l^2_{ref} $$ |
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The reference values of the highlighted variables in the table above are based on the solver and user-defined options.
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## Non-Dimensionalization Schemes (Compressible) ##
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| Solver | Version |
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| --- | --- |
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| `EULER`, `NAVIER_STOKES`, `RANS`,`FEM_EULER`, `FEM_NAVIER_STOKES` | 7.0.0 |
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The dimensionalization scheme can be set using the option `REF_DIMENSIONALIZATION`. For all schemes, the values set with `FREESTREAM_DENSITY` and `FREESTREAM_TEMPERATURE` are used as reference values for Density and Temperature, respectively, i.e. $$ \rho_{ref} = \rho_{\infty}, T_{ref} = T_{\infty}$$. The reference velocity is based on the speed of sound defined by the reference state: $$v_{ref} = \sqrt{\frac{p_{ref}}{\rho_{ref}}}$$.
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