Cell-limited gradient scheme

Properties

The cell gradient is limited to ensure that the face values obtained by extrapolating the cell value to the cell faces using the gradient are bounded by the neighbouring cells minimum and maximum limits.

As an example, consider the limiter to apply between cells P and N.

The value of $\phi_P$ is extrapolated using the gradient at P to the cell face $\phi_{f,e}$. When using a coefficient of 1, if the extrapolated value exceeds the value of the neighbour value $\phi_N$ the gradient is scaled so as to achieve $\phi_{N}$.

Usage

The scheme is specified using:

gradSchemes
{
    default         none;
    grad(U)         cellLimited <scheme> <coefficient>;
}

The coefficient should be specified in the range zero to one, where values of

• 1 represent limiting the gradient to ensure the extrapolated face value is bounded by the minimum and maximum neighbour cell values
• smaller values allow variation the extrapolated value to exceed the neighbour cell limiting values by a multiple of $\mathrm{max}(\phi_N) - \mathrm{min}(\phi_N)$

Further information

Source code

• Foam::fv::cellLimitedGrad

Mult-directional form

• cellMDLimited