Multiple computational schemes associated with the spatial interpolation in a collocated grid system are investigated in a MAC method. The simultaneous linear equations of the scalar potential φ=
pn+1-pn include the second derivatives of the pressure
pn discretized by the central difference with the interval of Δ
xi in the the CBP (Cell-Boundary Pressure) scheme, which utilizes
pn on cell boundaries in the prediction stage. However, the same derivatives are evaluated with the interval of 2Δ
xi in the CCP (Cell-Center Pressure) scheme that estimates the pressure gradient at the cell center points. It has been shown that the CCP scheme is likely to cause the free-surface or pressure instabilities, although the CBP scheme deals with them. Conclusively, the combination of the CBP scheme and PG scheme, which calculates
un+1i with the pressure gradient at the cell center points in the correction stage of the MAC method, is particularly effective together with the HSMAC method for the velocity-pressure relaxation.
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