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:
gradSchemes
{
default none;
grad(p) <optional limiter> <gradient scheme> <interpolation scheme>;
}
Options🔗
Gradient schemes🔗
Interpolation schemes🔗
-
linear
: cell-based linear -
pointLinear
: point-based linear -
leastSquares
: Least squares
Gradient limiters🔗
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
- Face-limited gradient scheme
- Multi-directional cell-limited gradient scheme
-
clippedLinear
: limits linear scheme according to a hypothetical cell size ratio
Example🔗
See this example to see the relative performance of the schemes.
Further information🔗
Source code:
API: