OpenFOAM guide/FvMatrix;;flux

A frequently performed operation in numerical algorithms, including SIMPLE and PISO, is the calculation of the face fluxes after the solution of the pressure equation:

$F = \mathbf S \bullet \left \lbrack \left . \frac{\mathbf H}{A_p} \right \vert_{v \to f} - \left . \frac{1}{A_p} \right \vert_{v \to f} \left . \boldsymbol \nabla p \right \vert_{v \to f} \right \rbrack$

Where:

• S are the surface area normal vectors;
• H is the H operator;
• A_p are the diagonal matrix coefficients from the U equation;
• p is the pressure; and
• $v \to f$ indicates interpolation from cell volume centres to face centres.

Uses lduMatrix;;faceH to calculate the individual components.