• Transactions of the Korean Society of Mechanical Engineers
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• v.8 no.3
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• pp.185-194
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• 1984

The finite analytic method is extended to solve the steady two dimensional Navier-Stokes equation of stream functions and vorticity in polar coordinate system. The method is applied to calculate laminar flows in a sector cavity where the motion is induced by the rotation of the outer wall. Numerical solutions are obtained in the range of Reynolds number 0 to 5000 and aspect ratios 0.50, 1.20, 1.60 and 1.92. The finite analytic method is verfied to be accurate and fast convergent at high Reynolds numbers. It is promising as a numerical method of viscous flows and heat transfer. Flows in sector cavities show different flow structures and formation of secondary vortex with aspect ratios and Reynolds numbers in comparison with rectangular cavities.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.73-80
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• 2009

This paper aims to study local and global structure of holomorphic flows on $\mathbb{C}^1$. At a singular point of a holomorphic flow, we locally sector the flow into parabolic or elliptic types. By the local structure of holomorphic flows, we classify all the possible types of topologies of $\omega$-limit sets.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.333-339
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• 2014

In this paper, we describe the characterizations of omega limit sets (= ${\omega}$-limit set) on $\mathbb{R}^2$ in detail. For a local real analytic flow ${\Phi}$ by z' = f(z) on $\mathbb{R}^2$, we prove the ${\omega}$-limit set from the basin of a given attractor is in the boundary of the attractor. Using the result of Jim$\acute{e}$nez-L$\acute{o}$pez and Llibre [9], we can completely understand how both the attractors and the ${\omega}$-limit sets from the basin.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.2
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• pp.101.1-101.1
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• 2012

Building a relativistic magnetohydrodynamic (RMHD) code based on upwind schemes has been a challenging project, because of the absence of analytic expressions of eigenvalues and eigenvectors. We found analytic expressions of eigenvalues and eigenvectors for adiabatic RMHD flows which are relatively simple and manageable. Especially, our eigenvectors can handle all degenerate points. Using these analytic forms, we built a code based on the total variation diminishing (TVD) scheme, and successfully performed one-dimensional shock tube tests.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.1
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• pp.66.2-66.2
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• 2012

Building a relativistic magnetohydrodynamic (RMHD) code based on upwind scheme is a challenging project, because eigenvalues and eigenvectors are not yet analytically given. Here, we present analytic expressions for eigenvalues and eigenvectors in isothermal flows. And then we show tests performed with a code based on the total variation diminishing (TVD) scheme.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.831-834
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• 2002

An analytic approach is attempted to predict the amplification of turbulence in compressible flows experiencing one-dimensional and axisymmetric bulk dilatation. The variations of vortex radius and vorticity are calculated, and then the amplification of turbulence is obtained from them by tracking three representative vortices. For a one-dimensionally compressed flow, the present analysis slightly underestimates the amplification of velocity fluctuations and turbulent kinetic energy, relative to that of rapid distortion theory in the solenoidal limit. For an axisymmetrically distorted flow, the amplification of velocity fluctuations and turbulent kinetic energy depend not only on the density ratio but also on the ratio of streamwise mean velocities, which represents streamwise vortex contraction/stretching. In all flows considered, the amplification of turbulence is dictated by the mean density ratio. In the axisymmetric flow, streamwise vortex stretching/contraction, however, alters the amplification slightly.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.156-161
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• 1998

This describes a numerical method for predicting the incompressible unsteady laminar three-dimensional flows of fluid behaviour with free-surface. The elliptic differential equations governing the flows have been linearized by means of finite-difference approximations, and the resulting equations have been solved via a fully-implicit iterative method. The free-surface is defined by the motion of a set of marker particles and interface behaviour was investigated by way of a 'Lagrangian' technique. Using the GALA concept of Spalding, the conventional mass continuity equation is modified to form a volumetric or bulk-continuity equation. The use of this bulk-continuity relation allows the hydrodynamic variables to be computed over the entire flow domain including both liquid and gas regions. Thus, the free-surface boundary conditions are imposed implicitly and the problem formulation is greatly simplified. The numerical procedure is validated by comparing the predicted results of a periodic standing waves problems with analytic solutions or experimental results from the literature. The results show that this numerical method produces accurate and physically realistic predictions of three-dimensional free-surface flows.

• Journal of computational fluids engineering
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• v.2 no.1
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• pp.1-7
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• 1997

A FA-FD hybrid method, developed for solving three-dimensional incompressible Navier-Stokes equations, is applied to calculate three-dimensional laminar flows through a square duct with a 90° bend. The method discretizes the convective terms in the primary flow direction with 3rd-order upwind finite-differences and the convective and diffusive terms in the transverse directions with the two-dimensional finite analytic method. The non-staggered grid system is used and the pressure-velocity coupling is achieved by a global iteration procedure based on the PISO algorithm. Detailed comparisons between the computed solutions and the available experimental data are given mainly for the velocity distributions at cross-sections in a 90° bend of a square duct with both fully developed and developing entry flows. Although the computational result shows generally a good agreement with the experimental data, there are some significant discrepancies underlining the necessity of more accurate numerical methods as well as reliable experimental data for their validation.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.10
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• pp.867-873
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• 2001

The purpose of this study is to find analytic solution of determining the optimal capacity (lot-size) of multiproduct acyclic multistage production and inventory system to meet the finished product demand under the constraint of finite intermediate storage. Intermediate storage is a practical way to mitigate the material flow imbalance through the line of supply and demand chain. However, the cost of constructing and operating storage facilities is becoming substantial because of increasing land value, environmental and safety concern. Therefore, reasonable decision-making about the capacity of processes and storage units is an important subject for industries. The industrial solution for this subject is to use the classical economic lot sizing method, EOQ/EPQ(Economic Order Quantity/Economic Production Quantity) model, incorporated with practical experience. But EOQ/EPQ model is not suitable for the chemical plant design with highly interlinked processes and storage units because it is developed based on single product and single stage. This study overcomes the limitation of the classical lot sizing method. The superstructure of the plant consists of the network of serially and/or parallelly interlinked non-continuous processes and storage units. The processes transform a set of feedstock materials into another set of products with constant conversion factors. A novel production and inventory analysis method, PSW(Periodic Square Wave) model, is applied to describe the detail material flows among equipments. The objective function of this study is minimizing the total cost composed of setup and inventory holding cost. The advantage of PSW model comes from the fact that the model provides a set of simple analytic solutions in spite of realistic description of the material flows between processes and storage units. the resulting simple analytic solution can greatly enhance the proper and quick investment decision for the preliminary plant design problem confronted with economic situation.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.3
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• pp.305-312
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• 2010

The aim of this study is to find an analytic solution to the problem of determining the optimal capacity of a batch-storage network to meet demand for finished products in a system undergoing joint random variations of operating time and batch material loss. The superstructure of the plant considered here consists of a network of serially and/or parallel interlinked batch processes and storage units. The production processes transform a set of feedstock materials into another set of products with constant conversion factors. The final product demand flow is susceptible to joint random variations in the cycle time and batch size. The production processes have also joint random variations in cycle time and product quantity. The spoiled materials are treated through regeneration or waste disposal processes. The objective function of the optimization is minimizing the total cost, which is composed of setup and inventory holding costs as well as the capital costs of constructing processes and storage units. A novel production and inventory analysis the PSW (Periodic Square Wave) model, provides a judicious graphical method to find the upper and lower bounds of random flows. The advantage of this model is that it provides a set of simple analytic solutions while also maintaining a realistic description of the random material flows between processes and storage units; as a consequence of these analytic solutions, the computation burden is significantly reduced. The proposed method has the potential to rapidly provide very useful data on which to base investment decisions during the early plant design stage. It should be of particular use when these decisions must be made in a highly uncertain business environment.