Laplacian schemes

Taking the Laplacian of a property $\phi$ is represented using the notation:

$$\laplacian \phi = \frac{\partial^2}{\partial x_1^2} \phi + \frac{\partial^2}{\partial x_2^2} \phi + \frac{\partial^2}{\partial x_3^2} \phi$$

or as a combination of divergence and gradient operators

$$\div \left( \Gamma \grad \phi \right)$$

where $\Gamma$ is a diffusion coefficient.

Usage

Laplacian schemes are specified in the fvSchemes file under the laplacianSchemes sub-dictionary using the syntax:

laplacianSchemes
{
    default         none;
    laplacian(gamma,phi) Gauss <interpolation scheme> <snGrad scheme>
}

All options are based on the application of Gauss theorem, requiring an interpolation scheme to transform coefficients from cell values to the faces, and a surface-normal gradient scheme.

Example

Further information

• See the implementation details to see how the schemes are coded.