• Journal of Korea Water Resources Association
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• v.36 no.3 s.134
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• pp.365-374
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• 2003

This is a study on application of a TVD-Mccormack scheme for the computation of one-dimensional dam-break flows. The TVD scheme not only has the ability to damp out oscillations, but also does not contain terms with adjustable parameters. Moreover, the TVD-McCormack scheme does not cause any additional difficulty when dealing with the source term of the equation and retains second-order accuracy in both space and time. In this study, by appropriately designing the limiter functions, the TVD property can be achieved, and numerical oscillations near a jump discontinuities can be eliminated or reduced. Also, this numerical scheme has less computational errors when the direction of the predictor-corrector step is in the same direction as the shock wane propagation.

• 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 the Society of Naval Architects of Korea
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• v.58 no.3
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• pp.182-190
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• 2021

Computational simulations of turbulent flows around a model ship have been performed to investigate an influence of TVD schemes on the accuracy of advective terms associated with ship resistances. Several TVD schemes including upwind, second-order upwind, vanLeer, and QUICK as well as a nonTVD linear scheme were studied by examining temporal and spatial characteristics of accuracy transition in adjacent cells to the hull. Even though vanLeer scheme was the most accurate among TVD schemes in both structured and unstructured grid systems, the ratio of accuracy switch from 2^nd order to 1^st order in vanLeer scheme was considerable compared with the 2^nd order linear scheme. Also, the accuracy transition was observed to be overally scattered in the unstructured grid while the accuracy transition in the structured grid appeared relatively clustered. It concluded that TVD schemes had to be carefully used in computational simulations of turbulent flows around a model ship due to the loss of accuracy despite its attraction of numerical stability.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.27 no.6
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• pp.406-418
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• 2015

The present modified FUNWAVE-TVD model, which is a modification to its previous version 2.1, is applied to solitary wave propagation and is tested against the experiments of Vincent and Briggs(1989) and Luth et al.(1994). The eddy viscosity breaking scheme is used for comparison with the existing study in the case of breaking experiment. The symmetry of wave-induced current is maintained when the modified model is employed to Vincent and Briggs(1989) breaking experiment, but the symmetry of wave-induced current in previous model is not maintained. A better agreement with the breaking experimental data is obtained in the modified model using eddy viscosity breaking scheme than the shock capturing breaking scheme using nonlinear shallow water equation. For comparison with the schemes in the model, the fourth order MUSCL-TVD scheme by Erduran et al.(2005) and the third order MUSCL-TVD scheme using minmod limiter is applied, and the numerical solutions of solitary wave are compared.

• Journal of Korea Water Resources Association
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• v.34 no.2
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• pp.187-195
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• 2001

In this study, a numerical model describing the shallow-water equations is newly developed by using a TVD scheme. The model has a second-order accuracy in time and space and is free from nonphysical oscillations, even in the vicinity of large gradients. Because a upwind based TVD scheme requires a Riemann solver, the HLLC scheme is employed in this model. To calibrate the applicability and accuracy, the developed model is used to simulate dam-break waves in an ideal channel and a sloshing flow n a paraboloidal basin. Agreements between numerical predictions and analytical solutions are very resonable.

• 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 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.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.22-27
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• 2006

This paper describes the development of the stream-tube based dispersion model for modeling contaminant transport in open channels. The operator-splitting technique is employed to separate the 2D contaminant transport equation into the pure advection and pure dispersion equations. Then the total variation diminishing (TVD) schemes are combined with the second-order Lax-Wendroff and third-order QUICKEST explicit finite difference schemes respectively to solve the pure advection equation in order to prevent the occurrence of numerical oscillations. Due to various limiters owning different features, the numerical tests for 1D pure advection and 2D dispersion are conducted to evaluate the performance of different TVD schemes firstly, then the TVD schemes are applied to experimental data for simulating the 2D mixing in a straight trapezoidal channel to test the model capability. Both the numerical tests and model application show that the TVD schemes are very competent for solving the advection-dominated transport problems.

• Proceedings of the Korea Water Resources Association Conference
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• 2002.05a
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• pp.633-639
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• 2002

• 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.