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.