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:
Where:
- subscript p is the cell index;
- subscript r are related cells^{[1]};
- 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:
Due to its prevalence in solver algorithms, OpenFOAM implements the H operator directly in its matrix classes, including: