Abstract
In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the local- truncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.
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The project supported by the China NKBRSF (2001CB409604)
The English text was polished by Yunming Chen
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Ren, Y., Jiang, Y., Liu, M. et al. A class of fully third-order accurate projection methods for solving the incompressible Navier-Stokes equations. ACTA MECH SINICA 21, 542–549 (2005). https://doi.org/10.1007/s10409-005-0074-2
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DOI: https://doi.org/10.1007/s10409-005-0074-2