• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.457-464
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• 1998

An alternative variational method for a steady tow-dimensional inviscid flow problem to determine the domain given the constant wall velocity and constant vorticity in the whole domain is presented. The uniqueness result is obtained for convex domains.

• Journal of Integrative Natural Science
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• v.6 no.1
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• pp.53-56
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• 2013

We are interested in the rate of convergence of solutions of 2D Navier-Stokes equations in a smooth bounded domain as the viscosity tends to zero under Navier friction condition. If the initial velocity is smooth enough($u{\in}W^{2,p}$, p>2), it is known that the rate of convergence is linearly propotional to the viscosity. Here, we consider the rate of convergence for nonsmooth velocity fields when the gradient of the corresponding solution of the Euler equations belongs to certain Orlicz spaces. As a corollary, if the initial vorticity is bounded and small enough, we obtain a sublinear rate of convergence.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.6
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• pp.765-771
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• 2002

This Paper presents numerical solutions of two-dimensional Euler equations for supersonic steady and unsteady flows with heat addition in a convergent-divergent duct, The Van Leer FVS (flux vector splitting) method in generalized coordinates is employed in order to calculate the inviscid strong shock waves caused by thermal choking. We discuss on transient characteristics, start and unstart phenomena caused by thermal choking, limit of equivalence ratio to avoid thermal choking and fluctuation of specific thrust caused by thermal choking. We prove that thermal choking is a serious problem in view of engine performance.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.307-310
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• 2002

A two-dimensional numerical method for inviscid two-fluid flows with evolution of density interface is developed, and an initially stationary two-dimensional fluid sheet surrounded by another fluid is studied. The Interface between two fluids is modeled as a vertex sheet, and the flow field u÷th the evolution of interface is solved by using vortex-in-cell/front-tracking method. The edge of the sheet Is pulled back into the sheet due to surface tension and a blob is formed at the edge. This blob and fluid sheet are connected by a thin neck. In the inviscid limit, such process of the blob and neck formation is examined in detail and their kinematic characteristics are summarized with dimensionless parameters. The edge recedes at $V=1.06({\sigma}/{\rho}h)^{0.5}$ and the capillary wave Propagating into the fluid sheet must be considered for bettor understanding of the edge receding.

• Journal of the Korean Society for Marine Environment & Energy
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• v.10 no.2
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• pp.107-111
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• 2007

A two-dimensional numerical method for inviscid two-fluid flows with evolution of density interface is developed, and an initially stationary two-dimensional fluid sheet surrounded by another fluid is studied. The interface between two fluids is modeled as a vortex sheet, and the flow field with the evolution of interface is solved by using vortex-in-cell/front-tracking method. The edge of the sheet is pulled back into the sheet due to surface tension and a blob is formed at the edge. This blob and fluid sheet are connected by a thin neck. In the inviscid limit, such process of the blob and neck formation is examined in detail and their kinematic characteristics are summarized with dimensionless parameters. The edge recedes at and the capillary wave propagating into the fluid sheet must be considered for better understanding of the edge receding.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.843-852
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• 2016

A vortex sheet is susceptible to the Kelvin-Helmhotz instability, which leads to a singularity at finite time. The vortex blob model provided a regularization for the motion of vortex sheets in an inviscid fluid. In this paper, we consider the blob model for viscous vortex sheets and present a linear stability analysis for regularized sheets. We show that the diffusing viscous vortex sheet is unstable to small perturbations, regardless of the regularization, but the viscous sheet in the sharp limit becomes stable, when the regularization is applied. Both the regularization parameter and viscosity damp the growth rate of the sharp viscous vortex sheet for large wavenumbers, but the regularization parameter gives more significant effects than viscosity.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.13 no.12
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• pp.1196-1204
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• 2001

The rivulet is a narrow stream of liquid flowing down a solid surface. When the rivulet\`s flow rate exceeds a certain limit, it tends to meander exhibiting the instability of its interface. This analysis performs a perturbation analysis of this meandering rivulet assuming an inviscid flow possessing contact angle hysteresis at the contact line. The analysis reveals that the contact angle hysteresis as well as the velocity difference across the inter-face, strongly induces the instability of the liquid interface. Moreover, when the rivulet veto-city is low, it is predicted that the axisymmetric disturbance amplifies more rapidly than the anti-axisymmetric disturbance, which explains the emergence of the droplet flow at the low velocity regime.

• Journal of Advanced Research in Ocean Engineering
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• v.1 no.3
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• Journal of the Korean Society for Marine Environment & Energy
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• v.3 no.2
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• pp.18-24
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• 2000

A two-dimensional numerical method for inviscid two-fluid flows with a significant entrainment into both directions is established, and the oil leakage from a non-pressurized underwater pipe is studied. The interface between two fluids is modeled at a vortex sheet. The flow field and the subsequent interface evolution are solved by using the vortex-in-cell method. For longer flow simulation with a realistic two fluids interaction, an efficient merging scheme is introduced. In the Boussinesq limit, the speed of the external fluid intrusion into the pipe is very close to the existing mathematical models, and the lock exchange is observed in spite of a significant roll-up of the interface and entrainments. It is believed that the developed method can be utilized effectively for further detailed studies on various two-fluid flows which are encountered in many different marine oil spill problems.