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

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

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