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

• Proceedings of the KSME Conference
• /
• 2001.06e
• /
• pp.404-409
• /
• 2001

An account of second-order fractional-step methods and boundary conditions for the incompressible Navier-Stokes equations is presented. The present work has aimed at (i) identification and analysis of all possible splitting methods of second-order splitting accuracy; and (ii) determination of consistent boundary conditions that yield second-order accurate solutions. It has been found that only three types (D, P and M) of splitting methods called the canonical methods are non-degenerate so that all other second-order splitting schemes are either degenerate or equivalent to them. Investigation of the properties of the canonical methods indicates that a method of type D is recommended for computations in which the zero divergence is preferred, while a method of type P is better suited to the cases when highly-accurate pressure is more desirable. The consistent boundary conditions on the tentative velocity and pressure have been determined by a procedure that consists of approximation of the split equations and the boundary limit of the result. The pressure boundary condition is independent of the type of fractional-step methods. The consistent boundary conditions on the tentative velocity were determined in terms of the natural boundary condition and derivatives of quantities available at the current timestep (to be evaluated by extrapolation). Second-order fractional-step methods that admit the zero pressure-gradient boundary condition have been derived. The boundary condition on the new tentative velocity becomes greatly simplified due to improved accuracy built in the transformation.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.2 no.1
• /
• pp.14-23
• /
• 2010

A numerical model was developed for simulating a three-dimensional multilayer hydrodynamic and thermodynamic model in domains with irregular bottom topography. The model was designed for examining the interactions between flow and topography. The model was based on the three-dimensional Navier-Stokes equations and was solved using the fractional step method, which combines the finite difference method in the horizontal plane and the finite element method in the vertical plane. The numerical techniques were described and the model test and application were presented. For the model application to the northern part of Ariake Sea, the hydrodynamic and thermodynamic results were predicted. The numerically predicted amplitudes and phase angles were well consistent with the field observations.

• Proceedings of the KSME Conference
• /
• 2000.11b
• /
• pp.745-750
• /
• 2000

A numerical code which can simulate unsteady, incompressible and 3-dimensional flows in an engine cylinder has been developed. The governing equations based on the cylindrical coordinate are discretized by the finite volume method with staggered variable arrangements. A geometric conservation rule is also incorporated into the simulation code in order to deal with a moving boundary problem. For the unsteady simulation, a fractional step method is adopted. The law of wall is applied to the wall boundaries and standard $k-\;{\varepsilon}$ model is used to describe the in-cylinder turbulent flow. The model cylinder has one eccentric port, flat piston and flat cylinder-head. The comparisons with experimental data show fairly well qualitative agreement.

• Water Engineering Research
• /
• v.3 no.1
• /
• pp.23-30
• /
• 2002

A numerical model for the solution of two-dimensional dam break problems using fractional step method is developed on unstructured grid. The model is based on second-order Weighted Averaged Flux(WAF) scheme with HLLC approximate Riemann solver. To control the nonphysical oscillations associated with second-order accuracy, TVD scheme with SUPERBEE limiter is used. The developed model is verified by comparing the computational solutions with analytic solutions in idealized test cases. Very good agreements have been achieved in the verifications.

• Journal of applied mathematics & informatics
• /
• v.32 no.1_2
• /
• pp.99-111
• /
• 2014

In this paper, we have taken step in the direction to establish weak, strong and strict converse duality theorems for three types of dual models related to multiojective fractional programming problems involving ($H_p$, r)-invex functions.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1725-1739
• /
• 2016

Abstract. Numerical solutions for the evolutionary space fractional order differential equations are considered. A predictor corrector method is applied in order to obtain numerical solutions for the equation without solving nonlinear systems iteratively at every time step. Theoretical error estimates are performed and computational results are given to show the theoretical results.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.16 no.12 s.117
• /
• pp.1192-1200
• /
• 2006

Viscoelastic damping materials are widely used to reduce noise and vibration because of its low cost and easy implementation, for examples, on the body structure of passenger cars, air planes, electric appliances and ships. To design the damped structures, the material property such as elastic modulus and loss factor is essential information. The four-parameter fractional derivative model well describes the dynamic characteristics of the viscoelastic damping materials with respect to both frequency and temperature. However, the identification procedure of the four-parameter is very time-consuming one. In this study a new identification procedure of the four-parameters is proposed by using an FE model and a gradient-based numerical search algorithm. The identification procedure goes two sequential steps to make measured frequency response functions(FRF) coincident with simulated FRFs: the first one is a peak alignment step and the second one is an amplitude adjustment step. A numerical example shows that the proposed method is useful in identifying the viscoelastic material parameters of fractional derivative model.

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.42 no.7 s.337
• /
• pp.35-40
• /
• 2005

This paper proposes a fractional-N phase-locked loop (PLL) frequency synthesizer using the 3rd order ${\Delta}{\sum}$ modulator for 900MHz medium speed wireless link. The LC voltage-controlled oscillator (VCO) is used for the good phase noise property. To reduce the lock-in time, a charge pump has been developed to control the pumping current according to the frequency steps and the reference frequency is increased up to 3MHz. A 36/37 fractional-N divider is used to increase the reference frequency of the phase frequency detector (PFD) and to reduce the minimum frequency step simultaneously. A 3rd order ${\Delta}{\sum}$ modulator has been developed to reduce the fractional spur VCO, Divider by 8 Prescaler, PFD and Charge pump have been developed with 0.25um CMOS, and the fractional-N divider and the third order ${\Delta}{\sum}$ modulator have been designed with the VHDL code, and they are implemented through the FPGA board of the Xilinx Spartan2E. The measured results show that the output power of the PLL is about -lldBm and the phase noise is -77.75dBc/Hz at 100kHz offset frequency. The minimum frequency step and the maximum lock-in time are 10kHz and around 800us for the maximum frequency change of 10MHz, respectively.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.6 no.4
• /
• pp.459-471
• /
• 1994

A numerical scheme solving the quasi-3D wave-induced circulation is presented. The governing equations have been solve implicitly using a fractional step method in conjunction with the approximate factroization techniques. The equation of each step was discretized by the finite volume scheme which yields more accurate and conservative approximations than the schemes based on finite differences. Examples of computed nearshore current patterns are presented to demonstrate the validity of the model for typical situations through comparison with laboratory experimental data (Gourlay. 1974).