Third-order Upwind Differencing
Another widely suggested improvement is known as third-order upwind differencing (see Kawamura et al. 1986).
The following example illustrates the essence of this discretization scheme.
 |
|
 |
(13.1) |
Higher order upwind is an emerging area of research in Computational Fluid Dynamics.
However, so far no unique suggestion has been evolved as an optimal method for a wide variety of problems. Interested readers are referred to Vanka (1987), Fletcher (1988) and Rai and Moin (1991) for more stimulating information on related topics.
One of the most widely used higher order schemes is known as QUICK (Leonard, 1979).
The QUICK scheme may be written in a compact manner in the following way
The fifth-order upwind scheme (Rai and Moin, 1991) uses seven points stencil along with sixth-order dissipation. The scheme is expressed as
 |
|
 |
(13.3) |
|
