# OpenFOAM guide/H operator

From OpenFOAMWiki

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: