Hi, I try to solve the energy equation. Central difference does not work(Pe in my proble is around 10,000). Now I want to try the power-law scheme given by the Patankar in his book. Has anybody tried this method? Is there a better way I can use? Thank you.

Lu Zhang

The power-law scheme at that Pe will give you the upwind scheme, that is assuming that Pe=density*velocity*dx/gamma. If Pe is greater than 10 at all points, you will end up using the upwind scheme anyway. I suggest you try that first.

Hi, Thank you for your help. I will try that.

Lu Zhang

Hi, The central scheme is known to be unstable and is not recommended for high Pe numbers. The Power law scheme works fine. However I recommend you to use the first-order upwind and second order central difference hybrid scheme which is stable for several classes of flows and is also easy to implement. Regards

Thank you.

Lu