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A few Computational Fluid Dynamics (CFD) codes implement the so called PISO (Pressure-Implicit with Splitting of Operators) algorithm for pressure-velocity coupling.

My concern is what is actual temporal order of accuracy of the algorithm?

It probably isn't enough to discretize time-dependent term in transport equations by second order algorithm (like second order Backward-Euler - BDF2), since we still use mass fluxes from the last time-step in the momentum equations?

Any suggestion of the papers that deal with this topic is welcome, or something relevant to this topic from projection/operator-splitting methods that would help to find an answer.

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    $\begingroup$ Don't cite me on this, but if I recall correctly, the PISO approach is second-order accurate in time because of the second step that corrects the momentum equation with the new mass fluxes. However, I am not fully sure of this, I'll try to find a reference. $\endgroup$
    – BlaB
    Mar 15 at 2:31

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