• 전자공학회논문지A
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• 제32A권3호
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• pp.143-151
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• 1995

The electrochemical impulse oscillations of the cathodic currents at the platinum group (Pt, Pd) electrode/(0.05M KHC$_{8}H_{4}O_{4}$) buffer solution interfaces have been studied using voltammetric, chronoamperometric, and electrochemical impedance methods. The periodic impulses of the cathodic currents are the activation controlled currents due to the hydrogen evolution reaction, and depend on the fractional surface coverage of the adsorbed hydrogen intermediate and potential. The oscillatory mechanism of the cathodic current impulses is connected with the unstable steady state of negative differential resistance. The widths and periods of the cathodic current impulses are 4ms or 5ms and 152.5ms or 305ms, respectively. The H$^{+}$ discharge reaction step is 38 or 61 times faster thatn the recombination reaction steps and the H$^{+}$ mass transport processes. The atom-atom recombination reaction step is twice faster thatn the atom-ion recombination reaction step. The two kinds of active sites corresponding to the atom-atom and atom-ion recombination reaction steps exist on the platinum group electrode surfaces.

• 대한수학회지
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• 제55권2호
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• pp.471-506
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• 2018

In this article, some projection methods (or fractional-step methods) are proposed and analyzed for the micropolar Navier-Stokes equations (MNSE). These methods allow us to decouple the MNSE system into two sub-problems at each timestep, one is the linear and angular velocities system, the other is the pressure system. Both first-order and second-order projection methods are considered. For the classical first-order projection scheme, the stability and error estimates for the linear and angular velocities and the pressure are established rigorously. In addition, a modified first-order projection scheme which leads to some improved error estimates is also proposed and analyzed. We also present the second-order projection method which is unconditionally stable. Ample numerical experiments are performed to confirm the theoretical predictions and demonstrate the efficiency of the methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권3호
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• pp.193-204
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• 2012

This paper is comparing numerical schemes for a differential equation with convection and fourth-order diffusion. Our model equation is $h_t+(h^2-h^3)_x=-(h^3h_{xxx})_x$, which arises in the context of thin film flow driven the competing effects of an induced surface tension gradient and gravity. These films arise in thin coating flows and are of great technical and scientific interest. Here we focus on the several numerical methods to apply the model equation and the comparison and analysis of the numerical results. The convection terms are treated with well known WENO methods and the diffusion term is treated implicitly. The diffusion and convection schemes are combined using a fractional step-splitting method.

• 한국전산구조공학회논문집
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• 제27권3호
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• pp.173-182
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• 2014

동역학의 새로운 변분이론인 혼합 합성 변분이론은 수학물리학을 비롯한 공학에 있어 초기치-경계치 문제해석에 광범위하게 적용될 수 있는 기반을 제공하는 것으로, 본 논문은 이 이론을 토대로 시간에 대한 이차의 형상함수가 적용된 시간 유한요소해석법을 개발하고 그 해석법의 수치특성 확인을 통해 향후 다양한 동적시스템 해석의 적용에 대한 가능성을 살펴보았다. 이를 위해 가장 기본적인 선형탄성의 단자유도계가 고려되었다. 에너지 보존시스템의 경우(비감쇠 시스템에 외력이 작용치 않는 경우), 제안된 알고리즘 모두는 time-step에 관계없이 안정적이며 수치감쇠가 없이 에너지와 모멘텀이 보존되는 symplecticity property를 가지고 있음을 확인할 수 있었고, 감쇠시스템인 경우, time-step이 점점 작아질수록 정확한 해에 빠르게 수렴하는 것을 확인하였다.

• Wind and Structures
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• 제15권3호
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• pp.189-208
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• 2012

Lock-in and drag amplification phenomena are studied for a flexible cantilever using a simplified fluid-structure interaction approach. Instead of solving the 3D domain, a simplified setup is devised, in which 2D flow problems are solved on a number of planes parallel to the wind direction and transversal to the structure. On such planes, the incompressible Navier-Stokes equations are solved to estimate the fluid action at different positions of the line-like structure. The fluid flow on each plane is coupled with the structural deformation at the corresponding position, affecting the dynamic behaviour of the system. An Arbitrary Lagrangian-Eulerian (ALE) approach is used to take in account the deformation of the domain, and a fractional-step scheme is used to solve the fluid field. The stabilization of incompressibility and convection is achieved through orthogonal quasi-static subscales, an approach that is believed to provide a first step towards turbulence modelling. In order to model the structural problem, a special one-dimensional element for thin walled cross-section beam is implemented. The standard second-order Bossak method is used for the time integration of the structural problem.

• 한국전산유체공학회지
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• 제10권1호
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• pp.45-50
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• 2005

A fundamental understanding of the flow around the wind turbine is important to investigate the performance of new type of wind turbine. This study presents the simulation of three dimensional flow fields around the Darius wind turbine as an example. Incompressible Navier-Stokes equations are used for this simulation. The rotating coordinate system that rotates in the same speed of the turbine is used in order to simplify the boundary condition on the blades. Additionally, the boundary fitted coordinate system is employed in order to express the shape of the blades precisely. Fractional step method is used to solve the basic equations. Third order upwind scheme is chosen for the approximation of the non-linear terms since it can compute the flow field stably even at high Reynolds number without any turbulence models. The flow fields obtained in this study are highly complex due to the three dimensionality and are visualized effectively by using the technique of the computer graphics.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
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• pp.228-229
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• 2003

Complex flow field around the Darius turbine rotating stationally are simulated by solving the three dimensional incompressible Navier-Stokes equation numerically. The rotating coordinate system is employed so that the boundary conditions on the blades of the rotor become simple. In order to impose the boundary condition on the blades precisely, the boundary fitted coordinate system is employed. Fractional step method is used to solve the basic equations. The complex flow fields due to the three dimensionality of the geometry of the turbine and the rotation of the turbine are obtained and they are visualized effectively by using the technique of the computer graphics.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 추계학술대회
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• pp.910-915
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• 2003

A Navier-Stokes equation solver for incompressible viscous flows with free surface is developed and tested. This is based upon a fractional time step method and a non-staggered finite volume formulation for unstructured meshes. For time advancement scheme, Adams -Bashforth method for convective term and Crank-Nicolson method for diffusive term are applied. The interface between two fluids with different fluid properties is tracked with Piecewise Linear Interface Calculation(PLIC) Volume-of-Fluid(VOF) methods. Computational results are presented for some test problems: the broken dam, the sloshing in a rectangular tank, the filling of a cylindrical tank.

• 대한기계학회논문집B
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• 제27권6호
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• pp.753-765
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• 2003

A finite element code for the numerical solution of the Navier-Stokes equation is parallelized by vertex-oriented domain decomposition. To accelerate the convergence of iterative solvers like conjugate gradient method, parallel block ILU, iterative block ILU, and distributed ILU methods are tested as parallel preconditioners. The effectiveness of the algorithms has been investigated when P1P1 finite element discretization is used for the parallel solution of the Navier-Stokes equation. Two-dimensional and three-dimensional Laplace equations are calculated to estimate the speedup of the preconditioners. Calculation domain is partitioned by one- and multi-dimensional partitioning methods in structured grid and by METIS library in unstructured grid. For the domain-decomposed parallel computation of the Navier-Stokes equation, we have solved three-dimensional lid-driven cavity and natural convection problems in a cube as benchmark problems using a parallelized fractional 4-step finite element method. The speedup for each parallel preconditioning method is to be compared using upto 64 processors.

• International Journal of Reliability and Applications
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• 제7권2호
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• pp.167-175
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• 2006

Effective and quick methods that are easy to carry out even by hand, or easy to be programmed by hand-held calculators are needed for assessing the sizes of contrasts of unreplicated $2^P$ factorial designs. Moreover, they have the advantage to use the original numerical measurements which makes the analysis easier to explain. Basically, Lenth (1989) is one of the most familiar of such quick and powerful methods. Later on, Aboukalam (2001) proposes under constant effects an alternative sophisticated method to Lenth's method. The proposed method is the supreme from two considerable powers. The first utmost indicates less inflation deficiency while the other utmost indicates less shrinkage deficiency. Also under constant effects, Al-Shiha (2006) introduces an alternative quick method which is less shrinkage deficiency while the inflation deficiency is the same. If effects are random, Aboukalam (2005) introduces an alternative quick method in which the first power is favored as long as the second power is within a small margin. In the spirit of quickness and fixed effects, this article adds another method which is supreme from the two considerable powers. The method is based on a one step of the scale-part of a suggested M-estimate for location. Explicitly, we suggest adapting the skipped median (ASKM) estimate. Critical values of ASKM-method, for several sample sizes often used, are empirically computed.