Browsing by Author "Kang, Kyungkeun"

Now showing 1 - 7 of 7
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    Conservative multigrid methods for Cahn-Hilliard fluids
    (2002-09) Kim, Junseok; Kang, Kyungkeun; Lowengrub, John
    We develop a conservative, second order accurate fully implicit discretization in two dimensions of the Navier-Stokes NS and Cahn-Hilliard CH system that has an associated discrete energy functional. This system provides a diffuse-interface description of binary fluid flows with compressible or incompressible flow components [44, 4]. In this work, we focus on the case of flows containing two immiscible, incompressible and density-matched components. The scheme, however, has a straightforward extension to multi-component systems. To efficiently solve the discrete system at the implicit time-level, we develop a nonlinear multigrid method to solve the CH equation which is then coupled to a projection method that is used to solve the NS equation. We analyze and prove convergence of the scheme in the absence of flow. We demonstrate convergence of our scheme numerically in both the presence and absence of flow and perform simulations of phase separation via spinodal decomposition. We examine the separate effects of surface tension and external flow on the decomposition. We find surface tension driven flow alone increases coalescence rates through the retraction of interfaces. When there is an external shear flow, the evolution of the flow is nontrivial and the flow morphology repeats itself in time as multiple pinchoff and reconnection events occur. Eventually, the periodic motion ceases and the system relaxes to a global equilibrium. The equilibria we observe appears has a similar structure in all cases although the dynamics of the evolution is quite different. We view the work presented in this paper as preparatory for the detailed investigation of liquid/liquid interfaces with surface tension where the interfaces separate two immiscible fluids [37]. To this end, we include a simulation of the pinchoff of a liquid thread under the Rayleigh instability at finite Reynolds number.
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    On regularity of stationary Stokes and Navier-Stokes equations near boundary
    (2001-07) Kang, Kyungkeun
    We obtain local estimates of the steady-state Stokes system "without pressure'' near boundary. As an application of the local estimates, we prove the partial regularity up to the boundary for the stationary Navier-Stokes equations in a smooth domain in five dimension.
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    On the Hölder continuity of solutions of a certain system related to Maxwell's equations
    (2001-07) Kang, Kyungkeun; Kim, Seick
    In this paper, we prove the Hölder continuity of weak solutions of a certain system arising from the Maxwell's equations in a quasi-stationary electromagnetic field.
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    On the regularity of solutions to a parabolic system related to Maxwell's equations
    (2002-06) Kang, Kyungkeun; Kim, Seick; Minut, Aurelia
    The goal of this paper is to establish H\"older estimates for the solutions of a certain parabolic system related to Maxwell's equations. Such an estimate is employed to get the local H\"older continuity of the magnetic field arising from Maxwell's equations in a quasi-stationary electromagnetic field, provided the resistivity of the material is continuous in time.
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    Regularity of axially symmetric flows in a half-space in three dimension
    (2002-01) Kang, Kyungkeun
    We study axially symmetric solutions with no swirl of the three dimensional Navier-Stokes equations in a half-space. We prove that suitable weak solutions in this case are Hölder continuous up to the boundary at all points except for the origin. For interior points this implies smoothness in the spatial variables. Hölder continuity at the origin remains as an open problem.
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    Unbounded normal derivative for the Stokes system near boundary
    (2002-02) Kang, Kyungkeun
    We study local boundary regularity for the Stokes system. We show that, unlike in the interior case, non-local effects can lead to a violation of local regularity in the spatial variables near the boundary.