11.2.2 Higher Order Difference Schemes

All higher order schemes are currently implemented by means of source based methods. They use the Upwind scheme as their base with any deviation from the upwind scheme being treated as a source term. The following schemes all use a third element to estimate the value of the dependent variable, $\phi$, on a face

$$\phi_f \; = \; F\,(\phi_C, \, \phi_D, \, \phi_U \, )$$ (11.50)

where the suffices C, D and U represent the elements on the upwind, downwind and "upwind upwind" side of the face. For a boundary face or a face where the upwind upwind element is external to the solution domain the upwind scheme is used.