• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.34 no.2
• /
• pp.479-492
• /
• 2014

In this study, was proposed a numerical scheme imposing exact solutions as the internal boundary conditions for the shallow-water flows over a discontinuous transverse structure such as a step. The HLLL approximate Riemann solver with the MUSCL was used for the test of the proposed scheme. Very good agreement was obtained between simulations and exact solutions for various problems of the shallow-water flows over a step. In addition, results by the numerical model showed good agreement with those of dam-break experiments over a step and stepped chute one. Developed model can simulate the shallow-water flows over discontinuous bottom such as a drop structure without additional rating curve or topography smoothing. Given the proper evaluations for the flow resistance by a step and the energy loss by the nappe flow in the future, could be simulated flooding and drying of the shallow-water flows over discontinuous topography such as a weir or the river road with retaining wall.

• Journal of Korea Water Resources Association
• /
• v.36 no.5
• /
• pp.777-785
• /
• 2003

A numerical model for the solution of two-dimensional free surface flow is developed on unstructured grid. By using fractional step method, the two-dimensional shallow water equations (SWE) are treated as two one-dimensional problems. Thus, it is possible to simulate computational hydraulic problems with higher computational efficiency. The one-dimensional problems are solved using upwind TVD version of second-order Weighted Averaged Flux (WAF) scheme with HLLC approximate Riemann solver. The numerical oscillations which are common with second-order numerical scheme are controlled by exploiting WAF flux limiter, Some idealized test problems are solved using this model and very accurate and stable solutions are obtained. It can be concluded as an efficient implement for the computation of SWE including dam break problems that concerning discontinuities, subcritical and supercritical flows and complex domain.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.31 no.4
• /
• pp.229-239
• /
• 2019

A model of landslides is developed using the shallow water equations to simulate time-dependent performance of landslides. The shallow water equations are derived using the (b, s) coordinate system which can be applied in both river and ocean. The finite volume scheme employing the HLL approximate Riemann solver and the total variation diminishing (TVD) limiter is applied to deal with the numerical discontinuities occurring in landslides. For dam-break water flow and debris flow, numerical results are compared with analytical solutions and experimental data and good agreements are observed. The developed landslide model is successfully applied to predict subaerial and submarine landslides. It is found that the subaerial landslide propagates faster than the submarine landslide and the speed of propagation becomes faster with steeper bottom slope and less bottom roughness.

• Journal of Korea Water Resources Association
• /
• v.44 no.10
• /
• pp.819-830
• /
• 2011

The multi-slope MUSCL, proposed by T. Buffard and S. Clain, determines slopes of conserved variables at each edge of a cell in the linear reconstructions of data. In this study, the second order accurate numerical model was developed according to the multi-slope MUSCL to solve the shallow water equations on the unstructured grids. The HLLL scheme of approximate Riemann solvers was used to calculate fluxes. For the review of the applicability of the developed model, the results of the model were compared to the 'isolated building test' and the 'model city flooding experiment' conducted as part of the IMPACT (Investigation of extreMe flood Processes And unCerTainty) project in Europe. There were limitations to predict abrupt rising of water depths by the resistance of model buildings and water depths at the specific locations among the buildings. But they were identified as the same problems also revealed in results of the other models to the same experiment. On the more refined meshes to the 'model city flooding experiment' simulated results showed good agreement with measurements. It was verified that the developed model simulated well the complex phenomena such as a dam-break problem and the urban inundation by flash floods.

• Journal of Korea Water Resources Association
• /
• v.43 no.1
• /
• pp.105-117
• /
• 2010

This paper presents a new and simple technique to perform MUSCL reconstruction for solving 2D shallow water equations. The modified MUSCL scheme uses weighted area ratio to apply non-uniform grid in stead of the previous method that equally distributed the difference of conservation variables to each interface. The suggested method can physically reconstruct conservation variables in case of uniform grid as well as non-uniform grid. In this study, Unsplit scheme applicable to unstructured grid is used and efficient slope limiter of TVD scheme is used to control numerical oscillation which can be occurred in modified MUSCL scheme. For accurate and efficient treatment of bed slope term, the modified MUSCL scheme is coupled with the surface gradient method. The finite volume model applied to suggested scheme is verified through a comparison between numerical solution and laboratory measurements data such as the simulations of isolated building test case and Bellos's dam break test case.

• Journal of Korea Water Resources Association
• /
• v.34 no.1
• /
• pp.45-55
• /
• 2001

Transcritical flow is a term intended to denote the existence of both supercritical and subcritical flows within a computational domain. The major problems that need to be addressed while modeling transcritical flows include handling the differing features of signal propagation in subcritical and supercritical flow regions and maintaining conservation. The present study proposes the implicit ENO method as a high-resolution scheme for transcritical flow. This implicit ENO scheme is based on the ENO method, a new class of uniformly high-order-accurate essentially non-oscillatory implicit scheme, which has the advantage of unconditional stability. The implicit ENO scheme has not been used for the transcritical flow in open channel until now. As a result of application to the hypothetical dam-break flow, the implicit ENO scheme was ploved to produce accurate results with good robustness even though in the case of verb strong shock wave.

• Journal of Korea Water Resources Association
• /
• v.42 no.4
• /
• pp.271-279
• /
• 2009

The objective of this study is to develop the scheme to apply one-dimensional finite volume method (FVM) to natural river with complex geometry. In the previous study, FVM using the Riemann approximate solver was performed successfully in the various cases of dam-break, flood propagation, etc. with simple and rectangular cross-sections. We introduced the transform the natural into equivalent rectangular cross-sections. As a result of this way, the momentum equation was modified. The accuracy and applicability of newly developed scheme are demonstrated by means of a test example with exact solution, which uses triangular cross-sections. Secondly, this model is applied to natural river with irregular cross-sections and non-uniform lengths between cross-sections. The results shows that the aspect of flood propagation, location and height of hydraulic jump, and numerical solutions of maximum water level are in good agreement with the measured data. Using the developed scheme in this study, existing numerical schemes conducted in simple cross-sections can be directly applied to natural river without complicated numerical treatment.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.28 no.5B
• /
• pp.575-589
• /
• 2008

In the present work, we investigate the hydrodynamic behavior of a turbulent bore, such as tsunami bore and tidal bore, generated by the removal of a gate with water impounded on one side. The bore generation system is similar to that used in a general dam-break problem. In order to the numerical simulation of the formation and propagation of a bore, we consider the incompressible flows of two immiscible fluids, liquid and gas, governed by the Navier-Stokes equations. The interface tracking between two fluids is achieved by the volume-of-fluid (VOF) technique and the M-type cubic interpolated propagation (MCIP) scheme is used to solve the Navier-Stokes equations. The MCIP method is a low diffusive and stable scheme and is generally extended the original one-dimensional CIP to higher dimensions, using a fractional step technique. Further, large eddy simulation (LES) closure scheme, a cost-effective approach to turbulence simulation, is used to predict the evolution of quantities associated with turbulence. In order to verify the applicability of the developed numerical model to the bore simulation, laboratory experiments are performed in a wave tank. Comparisons are made between the numerical results by the present model and the experimental data and good agreement is achieved.