• Journal of the Korean Society of Propulsion Engineers
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• v.7 no.1
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• pp.40-48
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• 2003

Large eddy simulation is used to investigate the compressible flow over a open cavity, The sub-grid scale stresses are modeled using the dynamic model. The compressible Navier-Stokes equations are solved with the sixth order accurate compact finite difference scheme in the space and the 4th order Runge-Kutta scheme in the time. The results show a typical flow pattern of the shear layer mode of oscillation over the cavity. The votical disturbances, the roll-up of vorticity, and impingement and scattering of vorticity at the downstream cavity edge can be seen in the shear layer. Predicted acoustic resonant frequency is in good agreement with that of the empirical formula. The mean flow streamlines are nearly horizontal along the mouth of the cavity. The pressure has its minimum value in the vortex core inside the cavity.

• Journal of the Korean Society of Propulsion Engineers
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• v.10 no.2
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• pp.1-14
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• 2006

Present study examines the numerical issues of cell structure simulation for various regimes of detonation phenomena ranging from weakly unstable to highly unstable detonations. Inviscid fluid dynamics equations with $variable-{\gamma} $ formulation and one-step Arrhenius reaction model are solved by a MUSCL-type TVD scheme and 4th order accurate Runge-Kutta time integration scheme. A series of numerical studies are carried out for the different regimes of the detonation phenomena to investigate the computational requirements for the simulation of the detonation wave cell structure by varying the reaction constants and grid resolutions. The computational results are investigated by comparing the solution of steady ZND structure to draw out the minimum grid resolutions and the size of the computational domain for the capturing cell structures of the different regimes of the detonation phenomena.

• The Pure and Applied Mathematics
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• v.6 no.2
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• pp.113-120
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• 1999

This paper studies the problem of an infinite confined aquifer which at time t ＜ 0 is assumed motionless. At time t = 0 crude oil seeps into the aquifer, thereby contaminating the valuable drinking water. Since the crude oil and water are im-miscible, the problem is posed as a one-dimensional two-phase unsteady moving boundary problem. A similarity solution is developed in which the moving front parameter is obtained by Newton-Ralphson iteration. A numerical scheme, involving the front tracking method, is devised employing the fourth order Runge-Kutta method. Comparison of the exact and numerical schemes shows an error of only 3%. Thus the developed numerical scheme is quite accurate in tackling more realistic problems where exact solutions are not possible.

• Journal of the Korean Geosynthetics Society
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• v.18 no.3
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• pp.69-77
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• 2019

This paper presents a new analytical model for estimating the free vibration of tapered friction piles. The governing differential equation for the free vibration of statically axially-loaded piles embedded in non-homogeneous soil is derived. The equation is numerically integrated by the Runge-Kutta method, and then the eigenvalue of natural frequency is determined by the Regula-Falsi scheme. For a cylindrical non-tapered pile, the computed natural frequencies compare well with the available data from literature. Numerical examples are presented to investigate the effects of the tapering, the skin friction resistance, the end condition of the pile, the vertical compressive loading, and the soil non-homogeneity on the natural frequency and mode shape of tapered friction piles.

• Journal of the Korean Physical Society
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• v.73 no.9
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• pp.1303-1309
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• 2018

In the present paper, we study the entropy analysis of boundary layer flow over a slender stretching sheet under the action of a non uniform magnetic field that is acting perpendicular to the flow direction. The effects of viscous dissipation and Joule heating are included in the energy equation. Using similarity transformation technique the momentum and thermal boundary layer equations to a system of nonlinear differential equations. Numerical solutions are obtained using the shooting and fourth-order Runge-Kutta method. The expressions for the entropy generation number and Bejan number are also obtained using a suggested similarity transformation. The main objective of this article is to investigate the effects of different governing parameters such as the magnetic parameter ($M^2$), Prandtl number (Pr), Eckert number (Ec), velocity index parameter (m), wall thickness parameter (${\alpha}$), temperature difference parameter (${\Omega}$), entropy generation number (Ns) and Bejan number (Be). All these effects are portrayed graphically and discussed in detail. The analysis reveals that entropy generation reduces with decreasing wall thickness parameter and increasing temperature difference between the stretching sheet and the fluid outside the boundary layer. The viscous and magnetic irreversibilities are dominant in the vicinity of the stretching surface.

• 한국가스학회:학술대회논문집
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• 1997.09a
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• pp.14-19
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• 1997

A numerical method for determining the temperature vartiation in a natural gas transmission line is presented. By considering an element of the gas pipeline and assuming radially lumped heat transfer at steady-state conditions, the energy equation is developed. The integration of the developed nonlinear differential equation is done numerically using the fourth order Runge-Kutta scheme. The results of the present study have been compared with the results of Coulter equations, and show a fairly good agreement.

• 한국전산유체공학회:학술대회논문집
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• 2001.10a
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• pp.1-9
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• 2001

In this paper, some numerical methods recently developed for gas-liquid two-phase flows are reviewed. And then, a preconditioning method to solve cavitating flow by the author is introduced. This method employs a finite-difference Runge-Kutta method combined with MUSCL TVD scheme, and a homogeneous equilibrium cavitation model. So that it permits to treat simply the whole gas-liquid two-phase flow field including wave propagation, large density changes and incompressible flow characteristic at low Mach number. Finally, numerical results such as detailed observations of the unsteady cavity flows, a sheet cavitation break-off phenomena and some data related to performance characteristics of hydrofoils are shown.

• 한국전산유체공학회:학술대회논문집
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• 1995.10a
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• pp.113-117
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• 1995

Viscous analysis on incompressible flows is performed using unstructured triangular meshes. A two-dimensional and axisymmetric incompressible Navier-Stokes equations are solved in time-marching form by artificial compressibility method. The governing equations are discretized by a cell-centered based finite-volume method. and a centered scheme is used for inviscid and viscous fluxes with fourth order artificial dissipation. An explicit multi-stage Runge-Kutta method is used for the time integration with local time stepping and implicit residual smoothing. Convergence properties are examined and solution accuracies are also validated with benchmark solution and experiment.

• 한국전산유체공학회:학술대회논문집
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• 2008.03a
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• pp.215-220
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• 2008

A numerical method for gas-liquid two-phase flow is applied to solve shock-bubble interaction problems. The present method employs a finite-difference Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL-TVD scheme. A homogeneous equilibrium cavitation model is used. By this method, a Riemann problem for shock tube was computed for validation. Then, shock-bubble interaction problems between cylindrical bubbles located in the liquid and incident liquid shock wave are computed.

• 한국전산유체공학회:학술대회논문집
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• 2008.10a
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• pp.215-220
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• 2008

A numerical method for gas-liquid two-phase flow is applied to solve shock-bubble interaction problems. The present method employs a finite-difference Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL-TVD scheme. A homogeneous equilibrium cavitation model is used. By this method, a Riemann problem for shock tube was computed for validation. Then, shock-bubble interaction problems between cylindrical bubbles located in the liquid and incident liquid shock wave are computed.