The open source CFD toolbox

The gradient of a scalar property $$\phi$$ is represented using the notation:

$\grad \phi = \vec{e}_1 \frac{\partial}{\partial x_1} \phi + \vec{e}_2 \frac{\partial}{\partial x_2} \phi + \vec{e}_3 \frac{\partial}{\partial x_3} \phi$

where the $$\vec{e}$$ vectors represent the unit vectors of the 3-D space.

# Usage

Gradient schemes are specified in the fvSchemes file under the gradSchemes sub-dictionary using the syntax:

{
default none;
}

# Options

## Interpolation schemes

• linear: cell-based linear
• pointLinear: point-based linear
• leastSquares: Least squares

The limited gradient schemes attempt to preserve the monotonicity condition by limiting the gradient to ensure that the extrapolated face value is bounded by the neighbouring cell values.

# Example

See this example to see the relative performance of the schemes.

# Further information

Source code:

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