higher order normal gradient at boundaries
 

Hi
as you may already know when you want to set a Neumann boundary condition in OpenFOAM (like fixed Gradient or mixed boundary condition), it uses a linear two point forward or backward definition of the gradient for solving the related equation.

gradient normal to face =
where delta is face-center to cell-center vector.

am I right about this? if I am wrong please correct me.

this method which OpenFOAM uses for calculating surface normal gradient is a second order accurate scheme, is there a way to include other points than cell-center and face-center in calculating this gradient and have a higher order more accurate gradient type boundary condition?

thanks