Korean J. Math.  Vol 27, No 1 (2019)  pp.193-219
DOI: https://doi.org/10.11568/kjm.2019.27.1.193

The second-order stabilized Gauge-Uzawa method for incompressible flows with variable density

Taek-cheol Kim, Jae-Hong Pyo


The Navier-Stokes equations with variable density are challenging problems in numerical analysis community.   We recently built the 2nd order stabilized Gauge-Uzawa method [SGUM] to solve the Navier-Stokes equations   with constant density and have estimated theoretically optimal accuracy. Also we proved that SGUM is unconditionally stable. In this paper, we apply SGUM to the Navier-Stokes equations with nonconstant variable density   and find out the stability condition of the algorithms. Because the condition is rather strong to apply to real problems, we consider Allen-Cahn scheme to construct unconditionally stable scheme. 


Gauge-Uzawa method, finite element method, pressure correction method, Allen-Cahn

Subject classification

65M12, 65M60, 76D05


This study was supported by 2016 Research Grant from Kangwon National University (No.520160376).

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