Central Differencing

For a central difference scheme, the convective flux is computed as:

(347)

where the geometric weighting factor is related to the mesh stretching. It would have a value of 0.5 for a uniform mesh.

Central differencing is formally second-order accurate. However it is prone to dispersive error and is beset with stability problems for most steady-state situations. The dispersive errors make it problematical for discretizing positive-definite quantities (such as temperature or turbulent kinetic energy) where overshoots cannot be tolerated.

A significant advantage of central differencing over second-order upwinding is that, when used to discretize velocity (not a positive definite quantity) it preserves turbulent kinetic energy. Therefore, it is useful scheme in large eddy simulation (LES), where upwind schemes cause turbulent kinetic energy to decay unnaturally fast.