Hi, can somebody tell me what is the order of approximation a power-law scheme (of Patankar); and is this scheme monotone?

I used the power law scheme in my phd thesis. The only thing it does is to decrease the molecular diffusivity (viscosity, conductivity, ...). Hence, the overall dissipation introduced by the upwind scheme is reduced leading to a better precision. Since you still have to use an upwind discretization of the convective term, You cannot say that this scheme is of order two.

If you keep using an upwind discretization of the convective term, the scheme is monotone.

For heat transfer problems, it is a good scheme. But, I would't you it to desing a plane....