The open source CFD toolbox
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.

# Further information

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