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Checker-board pressure in 1d?

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Old   August 27, 2014, 05:14
Default Checker-board pressure in 1d?
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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.

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Old   August 27, 2014, 08:42
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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.
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Old   August 27, 2014, 10:35
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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
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