Search

Although the discontinuous Galerkin (DG) methods have been widely applied as an effective numerical tool for hyperbolic conservation equations (e.g., shallow water equations (SWEs) and compressible Navier-Stokes equations), one of the well-known drawbacks is the inconvenience in the treatment of second or higher derivative terms. For this reason, since the beginning of DG in the 1970s, many researchers have made efforts in devising accurate and consistent schemes to incorporate the possible jumps in solutions for higher-order derivatives. The turbulent stress terms of the SWEs are expressed as second-order derivatives and cannot be neglected due to their practical importance. So far, as a traditional approach, a flux formulation has been applied in DG SWE modeling. However, it is often criticized for being inefficient in terms of memory and computation time. In this study, the BR2 scheme, a well-known primal formulation in the DG computational fluid dynamics community, was employed and combined with the implicit Euler backward difference scheme for SWEs. The developed model was applied to four benchmark problems (including channel contraction and diverging, partial dam-break flow, and curved channel flow), and good agreements were observed.

In this paper, we investigated the flow around vertical circular cylinders with the numerical simulation of shallow water equations. Since tsunami tidal waves have large potential energy due to height difference, the man-made structures near coast are heavily damaged during the propagation of waves. For the damage mitigation of natural disaster, a careful configuration of such obstructive structures is worthy of attention, and it is of great practical importance to provide numerical simulation based on the ideal models of natural or artificial structures in a coastal area. The simplified numerical models are listed as the single large cylinder and four small cylinders of double inline, double staggered, and single four arrangement with fixing the same blockage ratio. Among various up-to-date schemes, the fifth-order WENO scheme is selected with a ghost-cell immersed boundary method, which enabled the easy detection of the arbitrary body shapes emerged in background Cartesian grids. In addition, we proposed the non-reflecting characteristic boundary condition based on the characteristic compatibility equations derived in shallow water equations to suppress the unexpected reflection waves at the open boundary. The analysis on a benchmark problem on solitary wave reflection led to an expected validation with the present numerical model. Finally, reflection and diffraction of a tsunami wave are analyzed against a single and four cylinders of the same blockage density, and it is believed to reduce 20.80% points for the best case of single four cylinders in the view of dissipation ratio defined by the kinematic power.

One important issue in the approach with shallow water equations, which is not restricted to discontinuous Galerkin formulation, is the limitation to step geometries (discontinuous bathymetry), due to the hydrostatic assumption employed for the derivation of shallow water equations from the Navier-Stokes equations. In addition, the explicit Runge-Kutta time-stepping schemes do not come without any drawbacks even though the majority of discontinuous Galerkin applications have employed explicit ones due to simplicity. In this study, the recently developed implicit discontinuous Galerkin scheme is combined with the surface gradient method for steps (SGMS). The developed scheme is verified with flows over discontinuous bathymetry, i.e., vertical steps and weirs. For one-dimensional problems, the flows over a step and over a rectangular weir are simulated. As for two-dimensional problems, the flow over a weir and the dam-break flow over a step followed by the L-shaped and 45°-bend channels are simulated. The numerical solutions are compared with the experimental data. In all cases, good agreements were observed and the effectiveness of the developed scheme was verified.

Lee, H., 2021. Propagation of solitary wave around conical island in level-set finite element framework. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 16–20. Coconut Creek (Florida), ISSN 0749-0208. Though the solitary wave is a single wave, it consists of a complex spectrum of frequencies, which enables in-depth analysis and reliable generation both in the laboratory and in the numerical model. For these reasons, solitary waves are known to be a good candidate for the description of waves including tsunamis since they effectively model the important effects of the long wave on the coasts very well. In addition, it is supposed to propagate over constant depth without appreciable changes, allowing for consistent referencing of its offshore or incident wave height. In this study, the level-set scheme, which is combined with the incompressible Navier-Stokes solver based on the fractional step algorithm in the framework of the finite element method, was applied to the modeling of wave propagation and runup on a circular conical island. Unstructured hexahedral meshes were generated for this purpose and MPI (Message Passing Interface) based parallel algorithms were developed to accelerate the computation. The physical behavior of waves are discussed in detail and the numerical results (e.g., runup heights) are compared with the experimental data. The good agreements were observed.

The numerical solutions of shallow water equations are presented with implicit discontinuous Galerkin (IDG) method. The motivations for the development of an implicit scheme is stated. Details of the developed model is described including the spatial and temporal discretization, the approximate Riemann solver, and the slope limiter. For the validation of the model, the channel transition flow of contraction and expansion are carried out. As the last case study, the classical dam-break flow is simulated. In all cases, linear triangular meshes are employed and the implicit backward Euler time integration scheme is used. As an approximate Riemann solver, the Roe numerical flux is employed and a van Albada type gradient-reconstruction type slope limiter was applied. Good agreement was observed with experimental observations and exact solutions in all case studies.

Lee, H. and Lee, N., 2018. Lattice Boltzmann Simulation of Shallow Water Equations in Finite Element Framework. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 106–110. Coconut Creek (Florida), ISSN 0749-0208.The characteristic Galerkin finite element model for the discrete Boltzmann equation is developed for the depth-integrated shallow water equations. The lattice Boltzmann method (LBM) simulates microscopic collision and streaming of fluid particles and, then, evaluates the macroscopic velocity, pressure, etc. from the computed particle distribution. Due to the inherent geometric flexibility of the unstructured mesh in finite element method, the mesh clustering near large gradients and the numerical treatments of complex geometries has become possible. Some benchmark problems of practical importance (subcritical flow over hump, flow around cylinder, curved channel, etc.) are tested and the numerical results are in good agreement with previous experimental or analytic solutions.

Recent development of computing power and theoretical advances in computational fluid dynamics have made possible numerical simulations of water waves with full three-dimensional Navier-Stokes equations. In this study, an internal wave maker using the mass source function approach was combined with the level set finite element method for generation and propagation of water waves. The model is first applied to the two-dimensional linear wave generation and propagation. Then, it is applied to the three-dimensional simulation of the wave generation and the problem of wave force evaluation on the vertical wall. To effectively utilize computational resources and enhance the speed of execution, parallel algorithms are developed and applied for the three-dimensional problems. The results of numerical simulations are compared with theoretical values and good agreements are observed.

Access to safe drinking water is still unavailable to many people in developing countries. Biosand filter (BSF) is one of the most promising emerging point of use technologies. A large amount of organic matters is contained in their water source. The purpose of this study is to develop a hybrid BSF system, called as a trickling biosand filter (TBSF), which is combined with rock media as trickling filter to reduce organic matters ranged from CODcr 50 to 150 mg/L in source water. The effects of TBSF and BSF on the factors as CODcr, flux, turbidity, and DO are analyzed. Results showed that the effluent CODcr of TBSF was obtained 2.3–4.2 mg/L during 41 d. However, that of BSF fluctuated within 13.1–28.6 mg/L. DO in standing water of TBSF increased to average 7.8 mg/L while that of BSF decreased to average 1.2 mg/L. DO played an important role to activate microbial activity in trickling filter and to ripen Schmutzdecke layer to decrease constantly turbidity and Escherichia coli (E. coli) in TBSF, thoug...

The wet-dry scheme for moving boundary treatment is implemented in the framework of discontinuous Galerkin shallow water equations. As a formulation of approximate Riemann solver, the HLL (Harten-Lax-van Leer) numerical fluxes are employed and the TVB (Total Variation Bounded) slope limiter is used for the removal of unnecessary oscillations. As benchmark test problems, the dam-break problems and the classical problem of periodic oscillation in the parabolic bowl are solved with linear triangular elements and second-order Runge-Kutta scheme. The results are compared with exact solutions and the numerical solutions of previous study. For a more practical application, the implicit Runge-Kutta scheme is employed for the bottom friction terms and the moving shoreline in a rectangular basin of varying slopes is simulated. In all case studies, good agreement is observed with exact solutions or other well-known numerical solutions.

Numerical solutions of 1D and 2D shallow water equations are presented with Runge-Kutta Discontinuous Galerkin (RKDG) finite element method. For 1D problems, the transcritical flows such as dam-break flows and a flow over a bump with hydraulic jump were simulated and the numerical solutions were compared with the exact solutions. As a formulation of approximate Riemann solver, the Local Lax-Wendroff (LLF) fluxes were employed and minmod slope limiter was used for 1D flows. For 2D applications, the classical problems of lateral transition were simulated. The HLL (Harten — Lax — van Leer) fluxes were adopted and a van Albada type gradient-reconstruction type slope limiter was applied. For the time integration, 3rd-order and 2nd-order TVD Runge-Kutta schemes were used for 1D and 2D simulations, respectively. In all case studies, good agreement was observed.

With the increase of the frequency in large-scale floods and natural disasters, the demands for highly accurate numerical river models are also rapidly growing. Generally, flows in rivers are modeled with previously developed and well-established numerical models based on shallow water equations. However, the so-far-developed models reveal a lot of limitations in the analysis of discontinuous flow or flow which needs accurate modeling. In this study, the numerical shallow water model based on the discontinuous Galerkin method was applied to the simulation of one-dimensional transcritical flow, including dam break flows and a flow over a hump. The favorable agreement was observed between numerical solutions and analytical solutions.

Recent development of computing power and theoretical advances in computational fluid dynamics have made possible numerical simulations of water waves with full Navier-Stokes equations. In this study, an internal wave maker using the mass source function approach was combined with the level set finite element method for generation of waves. The model is first applied to the two-dimensional linear wave generation and propagation. Then, it is applied to the three-dimensional simulation of the same problem. To effectively utilize computational resources and enhance the speed of execution, parallel algorithms are developed and applied for the three-dimensional problem. The results of numerical simulations are compared with theoretical values and good agreements are observed.

This study presented the results of an application of a floodplain dynamic model to the Nakdong River, South Korea. At the Nakdong River, high flows are reduced by dams and the river bed is degraded. Both changes contribute toward the same result: the floodplain is hydraulically disconnected from the main channel and the morphology of the river has been modified. Such changes brought also to a deep modification in the riparian vegetation distribution, abundance and composition. The focus of the study is on the relationship between the hydrology alterations induced by dams and the successional changes in riparian vegetation. More in detail, the study attempts to adapt an existing dynamic floodplain vegetation model to the Nakdong ecosystem characteristics in order to single out what were the effects of the dam operations that led to a change in the riparian landscape. The dynamic model is targeted on Monsoon floodplain vegetation, it is developed upon a custom developed geoprocessing framework and supported by a standalone user interface. It simulates dynamics of floodplain vegetation communities based on different physical parameters. The general concept of the model is that a vegetation community will either undergo toward a maturation stage or will be destroyed (recycling or retrogression) if the magnitude of key physical parameters is greater than the threshold value for a specific community. The model has been calibrated using hydraulic data spanning the time period 1952–2007. The calibration results have been also used to investigate the impacts on the riparian vegetation given by dams operations. The findings of the research highlight that consecutive years of reduced maximum discharge allowed consistent vegetation colonization of riverine areas that were bare before the dam construction.

The free surface flow of two conceptual fish passage designs are investigated numerically by a level-set finite-element method. One design has a right-angled entrance from the reservoir to the fish passage chute, and the other has a curved-shaped entrance. The numerical results are validated with hydraulic experiments through comparison of the free surface location and the pressure distribution in the spillway. It is found that the right-angled design yields a curved free surface and pressure distribution in the vicinity of the entrance due to large strains, whereas the curved-shaped design yields a smooth flow transition with small strains. The negative pressure distributions near the ogee crest for both designs exhibit similar characteristics. Further downstream the free surface is elevated near the wall and is associated with counterrotating vortices. It is concluded that the curved-shaped design is favorable for fish passage because of the feature of a smooth flow transition with small strains.

We present a numerical method for free surface flows that couples the incompressible Navier-Stokes equations with the level set method in the finite element framework. The implicit characteristic-Galerkin approximation together with the fractional four-step algorithm is employed to discretize the governing equations. The schemes for solving the level set evolution and reinitialization equations are verified with several benchmark cases, including stationary circle, rotation of a slotted disk and stretching of a circular fluid element. The results are compared with those calculated from the level set finite volume method of Yue et al. , which employed the third-order essentially non-oscillatory (ENO) schemes for advection of the level set function in a generalized curvilinear coordinate system