<aside> 💡 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.