Surface-normal gradient schemes

The full gradient of a property $Q$ at a face can can be interpolated from the cell-based gradient. The surface-normal contribution is then represented by:

$$\snGrad Q = \vec{n} \dprod \left( \grad Q \right)_f$$

where $\vec{n}$ is the face unit normal. The stencil for the gradient calculation at the face, $f$, between cells P and N is described by the following figure: where the vector $\vec{d}$ joins the two cell centres. A variety of schemes are available that differ in their application based on the angle, $\theta$, between the $\vec{d}$ and $\vec{n}$ vectors, representing the degree of non-orthogonality.

Usage

Surface-normal gradient schemes are specified in the fvSchemesfile under the snGradSchemes sub-dictionary using the syntax:

snGradSchemes
{
    default         none;
    snGrad(Q)       <snGrad scheme>;
}

Options

• Corrected surface-normal gradient scheme
• Face-corrected surface-normal gradient scheme
• Limited surface-normal gradient scheme
• Orthogonal surface-normal gradient scheme
• Uncorrected surface-normal gradient scheme

Example

Further information

Source code:

• snGradScheme

API:

• Foam::fv::snGradScheme