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I understand the checkerboard effect due to the use of collocated grid arrangements in FVM. However, I wanted to know whether this problem is definitely bound to effect the results? For instance, I have modelled some problems on 1D structured grids with a collocated arrangement and have produced smooth results. Perhaps I am mistaken in how exactly the results should be effected?

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  • $\begingroup$ This depends on the problem. So unless you give more details about the equations you have in mind you will not get a meaningful answer. $\endgroup$ – Christian Waluga Nov 29 '15 at 17:25
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    $\begingroup$ I am interested to find out in general how does one decide whether or not to use collocated or staggered? Is it a trial and error procedure? For instance for the Euler equations governing a compressible flow at low mach numbers. $\endgroup$ – melody Nov 29 '15 at 22:38
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    $\begingroup$ I would say the question collocated or staggered is one of stability. Usually staggering helps to fulfill stability requirements in incompressible flow where the pressure is a Lagrange multiplier and inf-sup estimates are crucial. In compressible Euler scenarios I guess this is not an issue and you only need to look for suitable fluxes and limiters. But I am no expert on Euler equations. $\endgroup$ – Christian Waluga Dec 1 '15 at 6:51

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