Korean J. Math.  Vol 22, No 4 (2014)  pp.645-658
DOI: https://doi.org/10.11568/kjm.2014.22.4.645

A classification of the second order projection methods to solve the Navier-Stokes equations

Jae-Hong Pyo

Abstract


Many projection methods have been progressively con- structed to find more accurate and efficient solution of the Navier- Stokes equations. In this paper, we consider most recently con- structed projection methods: the pressure correction method, the gauge method, the consistent splitting method, the Gauge-Uzawa method, and the stabilized Gauge-Uzawa method. Each method has different background and theoretical proof. We prove equivalentness of the pressure correction method and the stabilized Gauge-Uzawa method. Also we will obtain that the Gauge-Uzawa method is equiv- alent to the gauge method and the consistent splitting method. We gather theoretical results of them and conclude that the results are also valid on other equivalent methods. 


Keywords


Projection method, Gauge-Uzawa method, the rotational form of pressure correction method, Navier-Stokes equations, incompressible fluids.

Subject classification

65M12, 65M15, 76D05

Sponsor(s)

This study was supported by 2014 Research Grant from Kangwon National University (No. 120140361).

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