On the stability and performance of the projection-3 method for the time integration of the Navier-Stokes equations

Michael Philip Kirkpatrick, S. W. Armfield

Abstract


The projection-2 method commonly used for the non-iterative time integration of the Navier--Stokes equations introduces a second order in time error. This error is reduced to third order when the projection-3 method is used. However, the projection-3 method can lead to solutions that are unbounded in time and, consequently, the projection-3 method has received little attention. This article compares the stability and performance of the projection-3 method with that of the projection-2 method. Both methods have been implemented in a Navier--Stokes solver that integrates the three dimensional equations on a staggered Cartesian grid. Time integration uses a second order hybrid Crank--Nicolson/Adams--Bashforth scheme. Results are presented for two test cases.

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DOI: http://dx.doi.org/10.21914/anziamj.v49i0.307



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