• Title/Summary/Keyword: incompressible flows with variable density

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

  • Kim, Taek-cheol;Pyo, Jae-Hong
    • Korean Journal of Mathematics
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    • v.27 no.1
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    • pp.193-219
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    • 2019
  • 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.

Calculations of Compressible Flows Using a Pressure Based Method (압력장에 기초한 수치해석 방법을 이용한 압축성 유동장의 수치해석)

  • Lim H. S.;Sah J. Y.;Kang D. J.
    • 한국전산유체공학회:학술대회논문집
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    • 1996.05a
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    • pp.27-32
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    • 1996
  • A previously developed pressure based calculation procedure for incompressible flows was modified and applied to transonic and supersonic flows. It uses pressure as a primary variable in preference to density and body fitted coordinate and non-staggered grid system. The discretized momentum equations were rearranged as a system of equations with respect to covariant velocity components. Three different discretization schemes, QUICK hybrid and first order upwind, were used to approximate the convective terms and compared. Present approach was tested far two transonic flow and one supersonic flow problems. Comparison with previous results show that present approach can be used as a solver for compressible flows.

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Multiple Unstable Modes in the Reacting Mixing Layer (반응혼합층의 복수 불안정성 모드)

  • Sin, Dong-Sin
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.20 no.2
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    • pp.616-623
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    • 1996
  • This paper investigates the linear stability of reacting mixing layers with special emphasis on the existence of multiple unstable modes. The governing equations for laminar flows are from two-dimensional compressible boundary-layer equations. The chemistry is a finite rate single step irreversible reaction with Arrhenius kinetics. For the incompressible reacintg mixing layer with variable density. A necessary condition for instability has been derived. The condition requires that the angular momentum, not the vorticity, to have a maximum in the flow domain. New inflectional modes of instability are found to exist in the outer part of the mixing layer. For the compressible reacting mixing layer, supersonic unstable modes may exist in the abscence of a generalized inflection point. The outer modes at high Mach numbers in the reacting mixing layer are continuations of the inflectional modes of low Mach number flows. However, the generalized inflection point is less important at supersonic flows.