• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.753-765
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• 2020

Smoking is one of the main causes of health problems and continues to be one of the world's most significant health challenges. In this paper, we use the multi-step Adomian decomposition method (MSADM) to obtain approximate analytical solutions for a mathematical fractional model of the evolution of the smoking habit. The proposed MSADM scheme is only a simple modification of the Adomian decomposition method (ADM), in which ADM is treated algorithmically with a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The solutions obtained are also presented graphically. The results reveal that the method is effective and convenient for solving linear and nonlinear differential equations of fractional order.

• 한국전산유체공학회지
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• 제15권4호
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• pp.99-108
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• 2010

Fractional Step Methods(FSM) are popular in simulation of unsteady incompressible flow. In this study, we demonstrate that FSM, combined with a Volume-Of-Fluid method, can be further applied to simulation of multiphase flow. The interface between the fluids is constructed by the effective least squares volume-of-fluid interface reconstruction algorithm and advected by the velocity using the operator split advection algorithm. To verify our numerical methodology, our results are compared with other authors' numerical and experimental results for the benchmark problems, revealing excellent agreement. The present FSM sheds light on accurate simulation of turbulent multiphase flow which is found in many engineering applications.

• 대한기계학회논문집B
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• 제27권4호
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• pp.458-465
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• 2003

The main objective of the research is to develop a research code solving transient incompressible Navier-Stokes equation. In this research code, Adams-Bashforth method was applied to the convective terms of the navier stokes equation and the splitted equations were discretized spatially by finite element methods to solve the complex geometry problems easily. To reduce the divergence on the boundaries of pressure poisson equation due to the unsuitable pressure boundary conditions, multi step approximation pressure boundary conditions derived from the boundary linear momentum equations were used. Simulations of Lid Driven Flow and Flow over Cylinder were conducted to prove the accuracy by means of the comparison with results of the previous workers.

• 한국해안해양공학회지
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• 제6권4호
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• pp.459-471
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• 1994

쇄파작용에 기인한 준 3차원적 연안류 순환 모델의 수치 기법을 제시한다. 지배 방정식은 근사 factorization 기법과 fractional step method를 사용하여 음해법으로 수치해석 되었고 분할된 식은 유한 체적법으로 차분된다. 계산된 3차원적 연안류 패턴의 한 예로서 Gourlay(1974)의 실험자료와 비교하여 간접적으로 모델의 타당성을 검증한다.

• 대한조선학회논문집
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• 제41권4호
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• pp.1-8
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• 2004

As a computer has been continuously progressed to reduce R&D time and cost, the study of the flow physics has been significantly relied on the numerical method. Recently, Large Eddy Simulation(LES) has been widely used in CFD community to accurately capture the turbulent flows. The LES code requires high accuracy in time, as well as in space. Also, it should have strong robustness to ensure the convergence in various complicated flows. The objective of the present work is to develop a base code for LES simulation, having 2$^{nd}$ order accuracy in time and 4$^{th}$ order accuracy in space. To achieve the present objective, the four-step fractional step method was enhanced by adopting compact Pade'scheme. The standard Smagorinsky model was implemented for the first stage of the present code development. The flows over a cylinder and an airfoil were successfully simulated. and an airfoil were successfully simulated.

• 대한기계학회논문집A
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• 제29권1호
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• pp.145-155
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• 2005

In this study, a finite element method program code which can be accomodate boundary conditions on the complex surfaces has been developed to simulate polymer extruder processes. The analysis method includes the fractional 4-step method for efficient computation time and compact usage of memory storage to solve the velocities and the pressure values from the Navier-Stokes equation. By using the developed program which was verified with simple Poiseuille flow mixture phenomena in single-and twin-screw extruder are analyzed. It is concluded that the proposed method resulte Poiseuille Poiseuille d in fair agreement with the exact solution of simple flow and the back flow near the entrance happens in single-screw model. It is identified that the location and values of maximum pressure in the twin screw extruder model. It is expected that the Velocity field found can be used to predict the degree of mixture in the extruder barrel.

• 한국해안해양공학회지
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• 제3권4호
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• pp.197-208
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• 1991

좌표변환된 깊이방향 평균 X-Y 수치모형을 수립하여 하구에서 염도확산을 분석하였다. 조간대의 수치적 모의, 잔차류, 폐경계조건 등이 검토되었으며, 특히 지배방정식 중 확산항의 처리에 시간분할방법(fractional step method)을 이용하여 수치해의 안정성 및 간편성을 도모하였다. 개발된 모형을 금강하구에 실제 적용하여 유속장과 염도장을 만족스럽게 재현시켰으며 유속장에 따른 확산계수산정에 대해서도 연구하였다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2009년 추계학술대회논문집
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• pp.1-1
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• 2009

In this presentation, I talk about various fluid simulation methods that have been developed for computer graphics special effects since 1996. They are all based on CFD but sacrifice physical reality for visual plausability and time. But as the speed of computer increases rapidly and the capability of GPU (graphics processing unit) improves, methods for more physical realism have been tried. In this talk, I will focus on four aspects of fluid simulation methods for computer graphics: (1) particle level-set methods, (2) particle-based simulation, (3) methods for exact satisfaction of incompressibility constraint, and (4) GPU-based simulation. (1) Particle level-set methods evolve the surface of fluid by means of the zero-level set and a band of massless marker particles on both sides of it. The evolution of the zero-level set captures the surface in an approximate manner and the evolution of marker particles captures the fine details of the surface, and the zero-level set is modified based on the particle positions in each step of evolution. (2) Recently the particle-based Lagrangian approach to fluid simulation gains some popularity, because it automatically respects mass conservation and the difficulty of tracking the surface geometry has been somewhat addressed. (3) Until recently fluid simulation algorithm was dominated by approximate fractional step methods. They split the Navier-Stoke equation into two, so that the first one solves the equation without considering the incompressibility constraint and the second finds the pressure which satisfies the constraint. In this approach, the first step introduces error inevitably, producing numerical diffusion in solution. But recently exact fractional step methods without error have been developed by fluid mechanics scholars), and another method was introduced which satisfies the incompressibility constraint by formulating fluid in terms of vorticity field rather than velocity field (by computer graphics scholars). (4) Finally, I want to mention GPU implementation of fluid simulation, which takes advantage of the fact that discrete fluid equations can be solved in parallel.

• Nuclear Engineering and Technology
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• 제56권4호
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• pp.1296-1309
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• 2024

The aim of this work is to explore the effect of the double subdiffusion on the stability in BWRs. A BWR novel reduced order model with double subdiffusion effects: reduced order fractional model (DS-F-ROM) to describe the neutron and heat transfer processes was proposed for this study. The double subdiffusion was developed with a fractional-order two-equation model, and with different fractional-orders and relaxation times. The stability analysis was carried out using the root-locus method and change from the s to the W domain and were confirmed using the time-domain evolution of neutron flux for a unit step change in reactivity. The results obtained using the reduced fractional-order model are presented for different anomalous diffusion coefficient values. Results are compared with normal diffusion and P1 equations, which are obtained straightforwardly with DS-ROM when relaxation time tends to zero, and when the anomalous diffusion coefficient tends to one, respectively.

• 한국해안해양공학회지
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• 제3권4호
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• pp.185-196
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• 1991

좌표변환된 측방향 평균 X-Z 수치모형을 수립하여 하구에서 염도확산을 분석하였다. 중력항과 깊이에 따른 밀도변화에 대한 검토와 염도 경계조건의 재평가 등이 이루어 졌으며, 특히 지배방정식중 확산항의 처리에 시간분별방법(fractional step method)을 이용하여 수치해의 안정성 및 간편성을 도모하였다. 개발된 모형을 금강하구에 실제 적용하여 Manning 계수·확산계수 등의 물리적 및 수치적인 특성을 조명하였고, 염도 확산범위를 비롯하여 갈수기의 영향과 대조 및 소조시 염도분포도 파악하였다.