Checker-board pressure in 1d?
 

Hey,

Do we have the checker-board problem in 1d. Looking at the problem it seems we would have it, but I am unsure and I have no possibility to write a small test code to check it. All my text books on CFD only describe a 2d case, so if a 1d case is described in a text please point me to it.

Best Regards

Yes, the checkerboard pressure pattern can occur in 1d given the same storage location of pressures and velocities and central-differencing of the pressure gradient.

yes, it occurs if you discretize d/dx(dp/dx) as

((dp/dx)|i+1 -(dp/dx)|i-1)/2dx = (p(i-2)-2p(i)+p(i+2))4dx^2