spurious oscillations and upwind-scheme

Chandra

hello,

I wrote my NS-equation solver and am testing it. (unsteady, 3D, incompressible, cylindrical co-ordinate). While solving the Energy equation, i found oscillations after using Central-Difference (CD) and no oscillations if Upwind-Scheme (UD). So, for the sake of better accuracy, I composed a hybrid scheme after mixing the two (25% UD, as follows) and found oscillations but very little amplitude as compared with CD scheme. Below is the hybrid scheme:

dT/dr = [dT/dr]_CD + ALPHA*(dx^2/2!)[d2T/dr2]_CD.

Here, "|ALPHA| = 1" for full upwind, "|ALPHA| = 0" for full central-difference and "0 < |ALPHA| < 1" for hybrid schemes. I used "|ALPHA| = 0.25".

To reduce the oscillation, one way is to increase |ALPHA|, say, to |ALPHA| = 0.5 and then do the computation.

What I want to know is: Can I expect BETTER accuracy if I use another scheme, say, Lax-Friedrichs with MUSCL reconstruction?? I saw very good results for shock-waves in this case.

In my case, for solution of the energy-equation, one wall is heated using a heater (20 kW/sq.m) and a water-jet is impinging normally on it. I don't know if this heated-wall boundary-condition is similar to a shock-like situation and whether the upwind-scheme is suitable for it. Based on your experience, please suggest me about this also.

Thank you very much,

regards, Chandra