• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.10
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• pp.2667-2677
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• 1995

A new numerical algorithm using equal order linear finite element and fractional step method has been developed which is capable of analyzing unsteady fluid flow and heat transfer problems. Streamline Upwind Petrov-Galerkin (SUPG) method is used for the weighted residual formulation of the Navier-Stokes equations. It is shown that fractional step method, in which pressure term is splitted from the momentum equation, reduces computer memory and computing time. In addition, since pressure equation is derived without any approximation procedure unlike in the previously developed SIMPLE algorithm based FEM codes, the present numerical algorithm gives more accurate results than them. The present algorithm has been applied preferentially to the well known bench mark problems associated with steady flow and heat transfer, and proves to be more efficient and accurate.

• Kyungpook Mathematical Journal
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• v.60 no.4
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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.

• Journal of Mechanical Science and Technology
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• v.14 no.5
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• pp.547-552
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• 2000

The objective of this paper is to present a modified fractional step method of keeping a constant mass flow rate in spatially periodic flows, because original fractional step methods do not precisely keep the mass flow rate constant in time. In the modified method, the mean and fluctuating pseudo-pressure gradients are separately obtained at each time step. This method is successfully applied to channel and pipe flows and shown to be suitable for maintaining a constant mass flow rate in time.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.410-415
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• 2001

An analytical and numerical examination of second-order fractional-step methods and boundary condition for the incompressible Navier-Stokes equations is presented. In this study, the compatibility condition for pressure Poisson equation and its boundary conditions, stability, and numerical accuracy of canonical fractional-step methods has been investigated. It has been found that satisfaction of compatibility condition depends on tentative velocity and pressure boundary condition, and that the compatible boundary conditions for type D method and approximately compatible boundary conditions for type P method are proper for divergence-free velocity for type D and approximately divergence-free for type P method. Instability of canonical fractional-step methods is induced by approximation of implicit viscous term with explicit terms, and the stability criteria have been founded with simple model problems and numerical experiments of cavity flow and Taylor vortex flow. The numerical accuracy of canonical fractional-step methods with its consistent boundary conditions shows second-order accuracy except $D_{MM}$ condition, which make approximately first-order accuracy due to weak coupling of boundary conditions.

• Journal of computational fluids engineering
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• v.15 no.4
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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.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.27-30
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• 2002

As computer capacity has been progressed continuously, the studies of the flow characteristics have been performing by the numerical methods actively. In this study, 3-dimensional unsteady incompressible Wavier-Stokes equation was solved by numerical method using the fractional step method with the fourth order compact pade' scheme to achieve high accuracy To validate the present code and algorithm, 3D flow-field around a cylinder was simulated. The drag coefficient and lift coefficient were computed and, then, compared with experiment. The present code will be tailored to LES simulation for more accurate turbulent flow analysis.

• 한국전산유체공학회:학술대회논문집
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• 2003.08a
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• pp.152-157
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• 2003

As computer capacity has been progressed continuously, the studies of the flow characteristics have been performing by the numerical methods actively. Recent numerical simulation has a tendency to require the higher-order accuracy in time, as well as in space. This tendency is more true in LES and acoustic noise simulation. In this study, 3-dimensional unsteady Incompressible Navier-Stokes equation was solved by numerical method using the fractional step method with the fourth order compact pade scheme to achieve high accuracy To validate the present code and algorithm, 3D flow-field around a cylinder was simulated. The drag coefficient and lift coefficient were computed and, then, compared with experiment. The present code will be tailored to LES simulation for more accurate turbulent flow analysis.

• Proceedings of the Korean Society of Rheology Conference
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• 2000.05a
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• pp.47-50
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• 2000

• Journal of computational fluids engineering
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• v.8 no.3
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• pp.50-55
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• 2003

Recent numerical simulation has a tendency to require the higher-order accuracy in time, as well as in space. This tendency is more true in LES and acoustic noise simulation. In the present work, the accuracy of a Fractional step method, which is widely used in LES simulation, has been increased to the fourth-order accurate compact Pade discretization. To validate the present code, the flow-field past a cylinder was simulated and compared with experiment. A good agreement with experiment was achieved.

• Journal of computational fluids engineering
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• v.10 no.2
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• pp.30-37
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• 2005

To evaluate LBM we performed the simulation of the unsteady two dimensional flow over a square cylinder in a channel in moderate Reynolds number range, $100\~500$ by using LBM and Fractional-Step method. Frist of all we compared LBM solution of Poiseuille flow applied Farout and periodic boundary conditions with the analytical solution to verify the applicability of the boundary conditions. For LBM simulation the calculation domain was formed by structured 500x100 grids. Prescribed maximum velocity and density inlet and Farout boundary conditions were imposed on the in-out boundaries. Bounceback boundary condition was applied to the channel and the cylinder waifs. The flow patterns and vortex shedding strouhal numbers were compared with previous research results. The flow patterns by LBM were in agreement with the flow pattern by fractional step method. Furthermore the strouhal number computed by LBM simulation result was more accurate than that of fractional step method through the comparison of the previous research results.