• Journal of applied mathematics & informatics
• /
• 제5권2호
• /
• pp.457-464
• /
• 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.

• 통합자연과학논문집
• /
• 제6권1호
• /
• pp.53-56
• /
• 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.

• 대한기계학회논문집B
• /
• 제26권6호
• /
• pp.765-771
• /
• 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.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2002년도 학술대회지
• /
• pp.307-310
• /
• 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.

• 한국해양환경ㆍ에너지학회지
• /
• 제10권2호
• /
• pp.107-111
• /
• 2007

경계를 가지는 비점성 2유체 유동을 해석할 수 있는 수치해법을 개발하고 이를 이용하여 초기에 정지되어 있는 액체판의 끝단에서 일어나는 수축현상을 분석하였다. 경계면은 보오텍스 쉬트로 모델하였고 유동장은 와도격자법과 경계면추적법을 적용하여 계산하였다. 액체판의 끝단은 표면장력에 의해 수축되고 뭉툭한 형상을 취하게 되고, 이러한 끝단은 잘룩한 형상의 통로에 의하여 액체판에 연결되어 안쪽으로 끌려들게 된다. 이러한 현상을 비점성 조건에서 운동에너지 변화를 포함한 무차원 수의 함수로 분석하였다. 끝단의 수축속도는 로 파악되었고 표면장력파의 전파특성이 엄밀하게 조사되어야 함을 밝혔다.

• 대한수학회보
• /
• 제53권3호
• /
• pp.843-852
• /
• 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.

• 설비공학논문집
• /
• 제13권12호
• /
• pp.1196-1204
• /
• 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
• /
• 제1권3호
• /
• pp.157-167
• /
• 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.

• 한국해양환경ㆍ에너지학회지
• /
• 제3권2호
• /
• pp.18-24
• /
• 2000

성질이 다른 두가지 유체가 복잡한 상호작용을 하는 경우의 유동을 살펴 보기 위하여 2차원 비점성 수치해법을 개발하고, 이를 감압된 수중 파이프에서의 기름 유출 문제에 적용하였다. 두 유체의 경계면은 보오텍스 쉬트로 모델링하고 보오텍스격자법 (vortex-in-cell method)을 적용하여 유동을 해석하며, 장시간의 유동 모사를 위하여 경계면의 분할과 접합이 가능하도록 하였다. Boussinesq 가정에서 외부유체의 관내로의 유입 속도가 기존의 수학모델과 거의 동일함을 확인하였고, 경계면에서의 복잡한 상호 유입과 보오텍스 유동에도 불구하고 Lock Exchange가 발생함을 보였다. 개발된 수치해법은 다양한 해양환경의 2상유체 문제에 효과적으로 이용될 수 있다고 사료된다.