Dear "Gurus"

I am trying to solve a 2-D flow over flat plat in conservation from of Navier-Stokes eqiuation using MacCormark's explicit method in finite difference.

My x and y grid sizes are of the order of 10^-7. The Raynold's number is 1000. Is this grid spacing all right? The value of Delta(t) is of the order of 10^-21.

But I am not getting the soluation all right. Something odd develops on alternate grids. For example.. velocities on even grids will be very HIGH (say 1200 m/s) and velocities on EVEN grids will be very LOW (say 0.0001 m/s).

Can somebody help me...PLEASE

Thanks

YOGESH

The symptoms you describe suggest the classic "checkerboard" instability. Check your pressure solution; does it also show a high-low alternating pattern?

This sort of problem is discussed extensively in Pat Roache' s book, Computational Fluid Dynamics (a classic - 1970's), so it should be well-covered in the modern texts.

Good luck!

Sir,

You have not commented on grid sapcing and delta(t).are they okey?

YOGESH

Are you talking about the MacCormack two-step predictor-correction scheme for compressible flows? If so, you may have some coding problems. Check carefully on the two steps and make sure they are NOT on the same time-level. In this scheme, each step is 1st order, one forward and one backward, at different time level. The two together makes it 2nd order. However, if the two steps are in the same time level, it becomes a 2nd order central-differening scheme. Then you will have this kind of odd-even grid points decoupling problem due to the lack of numerical dissipation (someone call artificial viscousity).

Your grid spacing may affect the accuracy but will not cause such probelm.

HL

Sir,

Actually I have misunderstood the situation. The real problem is.. The values spread tooo slowly in towards the internal grids. Suppose i have taken velocity at boundary to be 1300 m/s I find that only the points near boundary are affected and that to in a very slow manner.

Really speaking.. the very internal grid points are TOTALLY unaffected!

So i increased the time-step .. but then soln goes unstable. Shall i put number of iterations very high and time-step viz. Delta(t) very small?

Thank you

Yogesh