• 한국전산유체공학회:학술대회논문집
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• 1997.10a
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• pp.73-80
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• 1997

Objective of the present study is to examine the convergence characteristics of the various multi-stage Runge-Kutta methods in solving the incompressible Navier-Stokes equations of a time-marching from casted by the artificial compressibility method. Convergence characteristics are examined over 2-stage, 4-stage and hybrid type (using 4-, 3-, 2-stages sequentially) Runge-Kutta methods for a laminar lid-driven cavity flow, and also for a turbulent bump channel flow using Chien's low-Reynolds number turbulence model. Efforts are made to establish a stable and fast convergent multi-stage Runge-Kutta method with minimal artificial dissipations.

• Journal of computational fluids engineering
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• v.12 no.1
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• pp.43-52
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• 2007

A comparative study on flux functions for the 2-dimensional Euler equations has been conducted. Explicit 4-stage Runge-Kutta method is used to integrate the equations. Flux functions used in the study are Steger-Warming's, van Leer's, Godunov's, Osher's(physical order and natural order), Roe's, HLLE, AUSM, AUSM+, AUSMPW+ and M-AUSMPW+. The performance of MUSCL limiters and MLP limiters in conjunction with flux functions are compared extensively for steady and unsteady problems.

• 한국전산유체공학회:학술대회논문집
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• 2006.10a
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• pp.36-40
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• 2006

A comparative study on flux functions for the 2-dimensional Euler equations has been conducted. Explicit 4-stage Runge-Kutta method is used to integrate the equations. Flux functions used in the study are Steger-Warming's, van Leer's. Godunov's, Osher's(physical order and natural order), Roe's, HILE, AUSM, AUSM+ and AUSMPW+. The performance of MUSCL limiters and MLP limiters in conjunction with flux functions are compared extensively for steady and unsteady problems.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.3
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• pp.87-99
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• 1994

Reynolds Averaged Navier-Stokes equations are solved numerically for the computation of turbulent flow around a Wigley double model. A second order finite difference method is applied for the spatial discretization on the nonstaggered grid system and 4-stage Runge-Kutta scheme for the numerical integration in time. In order to increase the time step, residual averaging scheme of Jameson is adopted. Pressure field is obtained by solving the pressure-Poisson equation with the appropriate Neumann boundary condition. For the turbulence closure, 0-equation turbulence model of Baldwin-Lomax is used. Numerical computation is carried out for the Reynolds number of 4.5 million. Comparisons of the computed results with the available experimental data show good agreements for the velocity and pressure distributions.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• v.y2005m4
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• pp.343-346
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• 2005

Three dimensional structures of detonation wave propagating through a square-shaped duct were investigated using computational method and parallel processing. Inviscid fluid dynamics equations coupled with $variable-{\gamma}$ formulation and simplified one-step Arrhenius chemical reaction model were analysed by MUSCL-type TVD scheme and four stage Runge-Kutta time integration. The unsteady computational results in three dimension show the detailed mechanism of transverse mode and diagonal mode of detonation wave instabilities resulting same cell length but different cell width in smoked-foil record.

• Journal of computational fluids engineering
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• v.2 no.1
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• pp.8-12
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• 1997

The three-dimensional Euler equations are solved numerically for the analysis of contraction flows in wind or water tunnels. A second-order finite difference method is used for the spatial discretization on the nonstaggered grid system and the 4-stage Runge-Kutta scheme for the numerical integration in time. In order to speed up the convergence, the local time stepping and the implicit residual-averaging schemes are introduced. The pressure field is obtained by solving the pressure-Poisson equation with the Neumann boundary condition. For the evaluation of the present Euler solver, numerical computations are carried out for three contraction geometries, one of which was adopted in the Large Cavitation Channel for the U.S. Navy. The comparison of the computational results with the available experimental data shows good agreement.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.2
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• pp.202-212
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• 1997

In this study, performance of the multi-stage explicit methods for numerical computation of the unsteady Navier-Stokes equations is investigated. Three methods under consideration are 1 st-, 2 nd-, and 4 th-order Runge-Kutta (R-K) methods. Compared in this estimation is stability, accuracy, and CPU time of each method. The computational codes developed are applied to the two-dimensional flow in a square cavity driven by an oscillating lid. It turned out that at Reynolds number 400, the 1 st-order R-K method is the best, while at 3200 the 2 nd-order R-K is recommended. At higher Reynolds numbers, it is conjectured that the 4 th-order R-K method will be the best algorithm among three due to its highest stability.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.235-238
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• 2005

The unsteady supersonic flow over two- and three-Dimensional cavities has been analyzed by the integration of unsteady Reynolds-Averaged Navier-Stokes(RANS) with the k - w turbulence model. The unsteady flow is characterized by the periodicity due to the mutual relation between the shear layer and the internal flow in cavities. Numerical method is upwind TVD scheme based on the flux vector split with the Van Leer limiters, and time accuracy is used explicit 4th stage Runge-Kutta scheme. Cavity flows are Comparison of two- and three-dimensional. The cavity has a L/D ratio of 3 for two-dimensional case. and same L/D and W/D ratio is 1 for three-dimensional case. The Mach and Reynolds numbers are held constant at 1.5 and 450000 respectively. For the three-dimensional case, the flow field is observed to oscillate in the 'shear layer mode' with a feedback mechanism that follow Rossiter's formula. On the other hand, the self-sustained oscillating flow transitions to a 'wake mode' for the two-dimensional simulation, with more violent fluctuations inside the cavity.

• Journal of the Society of Naval Architects of Korea
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• v.38 no.1
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• pp.1-8
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• 2001

The computations of the turbulent flow around the ship models with the free-surface effects were carried out. Incompressible Reynolds-Averaged Navier-Stokes equations were solved by using an explicit finite-difference method with the nonstaggered grid system. The method employed second-order finite differences for the spatial discretization and a four-stage Runge-Kutta scheme for the temporal integration. For the turbulence closure, a modified Baldwin-Lomax model was exploited. The location of the free surface was determined by solving the equation of the kinematic free-surface condition using the Lax-Wendroff scheme and a free-surface conforming grid was generated at each time step so that one of the grid boundary surfaces always coincides with the free surface. An inviscid approximation of the dynamic free-surface boundary condition was applied as the boundary conditions for the velocity and pressure on the free surface. To validate the computational method developed in the present study, the computations were carried out for beth Wigley and Series 60 $C_B=0.6$ ship model and the computational results showed good agreements with the experimental data.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2003.10a
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• pp.95-98
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• 2003

The physics of the plume-induced shock and separation particulary at a high plume to exit pressure ratio and supersonic speeds up to Mach 3.0 with aid without a passive control method, porous extension, were studied using computational techniques. Mass-averaged Navier-Stokes equations with the RNG k-$\varepsilon$ turbulence model were solved using a fully implicit finite volume scheme and a 4-stage Runge-Kutta method. The courol methodology for plume-afterbody interactions is to use a perforated wall attached at either the nozzle exit or the edge of the missile base. The Effect of porous wall length on plume interference is also investigated. The computational results show the main effect of the porous extension on plume-afterbody interactions is to in the plume from strongly underexpanding during a change in flight conditions. With control, a change in porous extension length has no significant effect on plume interference.