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http://dx.doi.org/10.11568/kjm.2019.27.1.193

THE SECOND-ORDER STABILIZED GAUGE-UZAWA METHOD FOR INCOMPRESSIBLE FLOWS WITH VARIABLE DENSITY  

Kim, Taek-cheol (Department of Mathematics, Kangwon National University)
Pyo, Jae-Hong (Department of Mathematics, Kangwon National University)
Publication Information
Korean Journal of Mathematics / v.27, no.1, 2019 , pp. 193-219 More about this Journal
Abstract
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.
Keywords
incompressible flows with variable density; stability; projection methods; Gauge-Uzawa method; finite element method; pressure correction method; Allen-Cahn;
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