How can I estimate the local false diffusion in my mass transfer problems (see High Schmidt Number entry, below)? I'd like to use this information for selective grid refinement. One method of estimation is reviewed in Patankar's book from 1980 (page 108), but perhaps this is outdated. It provides surprisingly high values of false diffusion coefficient.

> ... It provides surprisingly high values of false diffusion coefficient. ...

and it's probably right! Remember, UD stabilises the discretisation by effectively dropping the Peclet number to 2 (or less). I've got some stuff in my Thesis about estimating numerical diffusion (and a-posteriori error estimation in general) - send me an E-mail if you want to know more.

Hrvoje

Dear Dr. Hrvoje Jasak:

I am also interested about the false diffusion. Your more detailed information will be very appreciated.

Regards

Maolin Tu

One of the ways of estimating how numerical diffusion affects the flow is to compute the energy and the momentum and to check how accurately they are conserved. You need to take into account forces acting on the flow, boundary conditions, etc...

For example for the energy, you can decide to check the integral in space (numerically) of 1/2*v**2*rho and see if it is conserved. That's a direct way of doing it.

In low order finite difference methods the results are 'poor', so don't be surprized if the numerical diffusion mentioned is so large.

Patrick