A divergence free fractional step method for the Navier-Stokes equations on non-staggered grids

Steven William Armfield, Nicholas Williamson, Michael Kirkpatrick, Robert Street


The Navier--Stokes equations may be discretised using finite-volume schemes on non-staggered or on staggered grids. Non-staggered grid schemes typically require a derivation that leads to an error in the divergence to prevent the occurrence of oscillations in the pressure field with accompanying problems in integration. The staggered grid does not have the problem of pressure oscillations; however, this is at the expense of increased code complexity. Two standard non-staggered schemes are compared to a modified scheme in which the divergence error does not occur.

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Navier-Stokes solver; Fractional step; Non-staggered grid

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DOI: https://doi.org/10.21914/anziamj.v51i0.2627

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