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* '''U''' is the uncorrected velocity; | * '''U''' is the uncorrected velocity; | ||
* '''S''' is the discretization source term; and | * '''S''' is the discretization source term; and | ||
− | * ''p''<sup>*</sup> is the | + | * ''p''<sup>*</sup> is the pressure from the previous timestep or initial guess. |
− | The '''H''' operator is all terms on the right-hand side, excluding those involving | + | The '''H''' operator is all terms on the right-hand side, excluding those involving pressure: |
<math>\mathbf H_p = \mathbf {S_m}_{,p} - \sum\limits_r A_r \mathbf{U}_r</math> | <math>\mathbf H_p = \mathbf {S_m}_{,p} - \sum\limits_r A_r \mathbf{U}_r</math> |
Revision as of 15:37, 30 June 2010
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: