OpenFOAM guide/H operator
The H operator is a form of shorthand notation that is not commonly used, but appears in OpenFOAM. It is comprised of a collection of terms from the momentum equation. A partially discretized form of the momentum equation is:
- subscript p is the cell index;
- subscript r are related cells;
- A are the matrix coefficients;
- U is the uncorrected velocity;
- S is the discretization source term; and
- p* is the pressure from the previous timestep or initial guess.
The H operator is all terms on the right-hand side, excluding those involving pressure:
Therefore the momentum equation becomes:
- 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.