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ðŸ’¡ The face contains all the Numerical Schemes in the program.

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## UPWIND Interpolation Scheme

These scheme is first order accurate and is used for convection dominated flows.

The formula for first-order UPWIND Scheme is as follows:

where

- flux_f is the flux at face of cell.
- flux_U is the flux at cell which is upstream of face.
- flux_D is the flux at cell which is downstream of face.
- flux_UU is the flux at cell after cell which is upstream of face.
- flux_DD is the flux at cell after cell which is downstream of face.

$$
flux_f = flux_U
$$

The flux value at face is the flux value at the Upwind cell centre.

## Central Differencing Interpolation Scheme

These scheme is second order accurate and is used for diffusion dominated flows.

The formula for CDS Scheme is as follows:

where

- flux_f is the flux at face of cell.
- flux_U is the flux at cell which is upstream of face.