• 한국전산유체공학회:학술대회논문집
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• 2003.08a
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• pp.11-17
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• 2003

The new multi-dimensional higher order interpolation scheme called MHIS is developed. Firstly, multi-dimensional TVD condition is derived based on one-dimensional TVD condition. Using multi-dimensional TVD condition, 2nd, 3rd and 5th order MHIS are presented. By help of multi-dimensional TVD condition, it is possible to captured a discontinuity monotonically even in a multi-dimensional flow. It is verified through several test cases that the accuracy and the robustness of MHIS are enhanced in regions of shock discontinuities as well as boundary-layers.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.30 no.4
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• pp.143-152
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• 2018

Numerical convergence and stability of TVD schemes have been applied in the FUNWAVE-TVD model were compared. The fourth order accurate MUSCL-TVD scheme using minmod limiter suggested by Yamamoto and Daiguji (1993), the fourth order accurate MUSCL-TVD scheme using van-Leer limiter suggested by Erduran et al. (2005) and the second order accurate MUSCL-TVD scheme using van-Leer limiter in Zhou et al. (2001) were compared. Comparisons of the numerical scheme were conducted with experimental data of Vincent and Briggs irregular wave experiments. In comparison with the fourth order accurate scheme using van-Leer limiter, the fourth order accurate scheme using minmod limiter is less dissipative but required lower CFL condition for stable numerical solution. On the other hand, the scheme using van-Leer limiter required smaller resolution spatial grid due to numerical dissipation, but relatively higher CFL condition can be used compared to the scheme using minmod limiter. In the breaking wave experiments which were conducted using high resolution spatial grid to reduce numerical dissipation, the characteristic of the schemes can be clearly observed. Numerical instabilities and blow-up of the numerical solutions were found in the irregular wave breaking simulation with the scheme using minmod limiter. However, the simulation can be completed with the scheme using van-Leer limiter, but required low CFL condition. Good agreements with the observed data were also observed in the results using van-Leer limiter.

• Journal of Korea Water Resources Association
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• v.34 no.2
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• pp.177-186
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• 2001

By using he total variation diminishing (TVD) condition, accurate and upwind based schemes are firstly introduced to develop numerical models free from nonphysical oscillations in the vicinity of large gradients. These models are then applied to both abruptly and smoothly varying initial conditions. By comparing computed predictions to analytical solutions, it is clearly shown that the first-order upwind scheme produces the numerical viscosity and the second-order Lax-Wendroff scheme produces the spurious oscillations. However, the TVD scheme gives the most reasonable results.

• Journal of Korea Water Resources Association
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• v.36 no.4
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• pp.597-608
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• 2003

A transcritical flow occurs when the width and slope of a channel are varying abruptly. In this study, the transcritical flow in a two-dimensional open channel is analyzed by using the shallow-water equations. A weighted average flux scheme that has flux limiter with a total variation diminishing condition is introduced for a second-order accuracy in time and space, and non- spurious oscillations at discontinuous points. A HLLC method with three wane speeds is employed to calculate the Riemann problem. To overcome difficulties resulting from variation of channel sections in a two-dimensional analysis of transcritical flow, the numerical model is developed based on a generalized grid system.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.9
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• pp.12-26
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• 2004

A new treatment of cell-interface flux in AUSM-type methods is introduced to reduce the numerical dissipation. Through analysis of TVD limiters, a criterion for the more accurate prediction of cell-interface state is found out and M-AUSMPW+ is developed by determining the transferred property newly and appropriately within the criterion. The superiority of M-AUSMPW+ is clearly revealed in multi-dimensional flow problems. It can eliminate numerical dissipation effectively in a non-flow aligned grid system. As a result, M-AUSMPW+ is shown to be much more accurate and effective than other previous schemes in multi-dimensional problems. Through a stationary contact discontinuity, a vortex flow, a shock wave/boundary layer interactions and viscous shock tube problems, it is verified that accuracy of M-AUSMPW+ is improved.

• Journal of computational fluids engineering
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• v.12 no.2
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• pp.53-62
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• 2007

A high resolution numerical method aimed at solving cavitating flow is proposed and applied to gas-liquid two-phase shock tube problem. The present method employs a finite-difference 4th-order Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL TVD scheme. By applying the homogeneous equilibrium cavitation model, the present density-based numerical method permits simple treatment of the whole gas-liquid two-phase flow field, including wave propagation and large density changes. The speed of sound for gas-liquid two-phase media is derived on the basis of thermodynamic relations and compared with that by eigenvalues. By this method, a Riemann problem for Euler equations of one dimensional shock tube was computed. Numerical results such as detailed observations of shock and expansion wave propagations through the gas-liquid two-phase media at isothermal condition and some data related to computational efficiency are made. Comparisons of predicted results and exact solutions are provided and discussed.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.36 no.1
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• pp.11-19
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• 2024

In this study, the program was modified by adding the empirical formula of EurOtop (2018) to enable calculation of wave overtopping on armoured slope structures in the FUNWAVE-TVD model using the fully nonlinear Boussinesq equation. The validity of the modified numerical model was verified by comparing it with CLASH data and experiment data for the rubble mound structure. This model accurately reproduced the change in wave overtopping rate according to the difference in the roughness factor of the armoured block, and well reproduced the rate of decrease in wave overtopping rate due to the increase in relative freeboard. The overtopping rate of the armoured slope structures showed significant differences depending on the positioning condition of the armoured blocks. When Tetrapods were placed with regular positioning, the overtopping rate increased significantly compared to when they were placed with random positioning, and it was consistent with when they were placed with Rocks. Meanwhile, when rocks were placed in one row, the wave overtopping rate was greater than when rocks were placed in two rows, which is believed to be due to the influence of the roughness and permeability of the structure's surface.

• Journal of computational fluids engineering
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• v.19 no.3
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• pp.91-97
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• 2014

A high resolution numerical method aimed at solving cavitating flow was proposed and applied to gas-liquid two-phase shock tube problem with arbitrary void fraction. The present method with compressibility effects employs a finite-difference 4th-order Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL TVD scheme. The Jacobian matrix from the inviscid flux of constitute equation is diagonalized analytically and the speed of sound for the two-phase media is derived by eigenvalues. So that the present method is appropriate for the extension of high order upwind schemes based on the characteristic theory. By this method, a Riemann problem for Euler equations of one dimensional shock tube was computed. Numerical results of high speed flow phenomena such as detailed observations of shock and expansion wave propagations through the gas-liquid two-phase media and some data related to computational efficiency are made. Comparisons of predicted results and solutions at isothermal condition are provided and discussed.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.49-54
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• 1998

3-dimensional Euler solver is parallelized. The spatial discretization method is the 2nd order TVD scheme and DADI method with multigrid is used as a time integration. In order to parallelize this solver, the domain decomposition method with overlapped grid and message passing techniques are used. The informations on the each inter-processor bound-aries are communicated with MPI library. Finally, the parallel performance repsented by calculating the ONERA M6 wing at transonic flow condition using CRAY T3E and C90.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.128-134
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• 2005

In the CFD area, the numerical analysis of high Mach number flow over a blunt-body poses many issues. Various numerical schemes have been developed to cover the issues, but the traditional schemes are still used widely due to the complexities of new schemes and intricacy of modifying the established codes. In the present study, the well-known Roe's FDS based on TVD-MUSCL scheme is used for the solution of very high Mach number three-dimensional flows posing carbuncle and non-physical phenomena in numerical analysis. A parametric study was carried out to account for the effects of the entropy fixing, grid configurations and initial condition. The carbuncle phenomena could be easily overcome by the entropy fixing, and the non-physical solution could be eliminated by the use of the modified initial condition regardless of entropy fixing and grid configurations.