Gradient schemes

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.

Gradient schemes are specified in the fvSchemes file under the `gradSchemes`

sub-dictionary using the syntax:

gradSchemes

{

default none;

grad(p) <optional limiter> <gradient scheme> <interpolation scheme>;

}

- 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.

- Cell-limited gradient scheme
- Multi-directional cell-limited gradient scheme
- Face-limited gradient scheme
- Multi-directional face-limited gradient scheme
- clippedLinear: limits linear scheme according to a hypothetical cell size ratio

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

Source code:

Would you like to suggest an improvement to this page? | Create an issue |

Copyright © 2016 OpenCFD Ltd.