OpenFOAM guide/FvMatrix;;H

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An implementation of the H operator, an off-diagonal function used in linearizing the convection term. The momentum equation can be expressed as:

A_p \mathbf{U}_p =
\mathbf{H}(\mathbf{U}) - \Delta p


  • The subscript p is the cell volume index;
  • A are discretization coefficients;
  • U is velocity;
  • p is pressure; and
  • H is given by:

By face index:

\mathbf{H}_{o,i} = A_{n,i} \boldsymbol \psi_{n,i} + \mathbf{S}_i

\mathbf{H}_{n,i} = A_{o,i} \boldsymbol \psi_{o,i} + \mathbf{S}_i


By cell volume index:

\mathbf{H}_p = \sum\limits_r A_r \boldsymbol \psi_r + \mathbf{S}_p


  • r are related cells[1].

The calculation of the sum of related cells is performed by lduMatrix;;H.


  1. What I'm calling related cells is conventionally called neighbours. But OpenFOAM has a different meaning for neighbours, so the term related cells is used.