• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 1999.03b
• /
• pp.253-256
• /
• 1999

The Streamline Upwind Petrov-Galerkin(SUPG) finite element method is used to solve the two-dimensional laminar and turbulent flow. The flow is simulated by averaged Navier-Stokes equations with a penalty function approach and the lograithmic(k-$\varepsilon$) turbulent model is employed to take into account its turbulent behavior. The near-wall viscous sub-layer model is employed to approach the dominant viscous effects in the near wall zones. To find a good-enough initial guess of the Newton-Raphson iteration solving Nonlinear Matrix the Incremental method is considered for momentum and the Incomplete logarithmic turbu-lent equations for Turbulence. The validation of our method is investigated in comparision with published experimental data.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2010.05a
• /
• pp.749-753
• /
• 2010

본 논문에서는 하천에 유입되는 오염물질 중 대부분을 차지하는 비보존성 오염물질의 확산거동을 분석하기 위해 2차원 수심 평균된 이송분산방정식에 유한요소법을 적용하였다. 수치모형 구성을 위해 SUPG(Streamline-upwind Petrov-Galerkin)법을 이용한 가중잔차법을 사용하였다. 모의대상 수질인자는 BOD와 DO이며, BOD 농도 결과가 DO 농도 계산에서의 입력 자료로 이용되도록 상호 연계를 형성하였다. 모형의 검증을 위하여 직사각형 수로에 선원으로 연속주입하여 얻은 수치해와 해석해를 비교하였다. 비교결과 수치해와 해석해의 결과가 서로 일치하는 것을 볼 수 있었다.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2005.05b
• /
• pp.414-418
• /
• 2005

A finite element model is developed for the numerical simulation of bed elevation change in a curved channel. The SU/PG (Streamline-Upwind/Petrov-Galerkin) method is used to solve 2D shallow water equations and the BG (Bubnov-Galerkin) method is used for the Exner equation. For the time derivative terms, the Crank-Nicolson scheme is used. The developed model is a decoupled model in a sense that the bed elevation does not change simultaneously with the flow during the computational time step. The total load formula with is used for the sediment transport model. The slip conditions are described along the lateral boundaries. The effects of gravity force due to geometry change and the secondary flows in a curved channel are considered in the model. For the verification, the model is applied to two laboratory experiments. The first is $140^{\circ}$ bended channel data at Delft Hydraulics Laboratory and the second is $140^{\circ}$ bended channel data at Laboratory of Fluid Mechanics of the Delft University of Technology. The finite element grid is constructed with linear quadrilateral elements. It is found that the computed results are in good agreement with measured data, showing a point bar at the inner bank and a pool at the outer bank.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.32 no.10
• /
• pp.754-760
• /
• 2008

Computation of moving interface by the level set method typically requires the reinitialization of level set function. An inaccurate estimation of level set function $\phi$ results in incorrect free-surface capturing and thus errors such as mass gain/loss. Therefore, an accurate and robust reinitialization process is essential to the simulation of free-surface flows. In the present paper, we pursue further development of the reinitialization process, which evaluates level set function directly using a normal vector on the interface without solving there-distancing equation of hyperbolic type. The Taylor-Galerkin approximation and P1P1 splitting/SUPG (Streamline Upwind Petrov-Galerkin) FEM are adopted to discretize advection equation of the level set function and the incompressible Navier-Stokes equation, respectively. Advection equation and re-initialization process of free surface capturing are validated with benchmark problems, i.e., a broken dam flow and timereversed single vortex flow. The simulation results are in good agreement with the existing results.

• Journal of Korea Water Resources Association
• /
• v.42 no.12
• /
• pp.1053-1067
• /
• 2009

The objective of this study is to develop an efficient and accurate quadratic finite element model based on Streamline Upwind/Petrov Galerkin (SU/PG) scheme for analyzing and predicting two dimensional flow features in complex natural rivers. For a development of model, quadratic tin, quadrilateral and mixed elements as well as linear tin, quadrilateral and mixed elements were used in the model. Also, this model was developed through reinforcement of Gauss Quadrature which was necessary to integral of governing equation. Several tests for bottom-rising channel and U-type channel were performed for the purpose of validation and verification of the developed model. Such results showed that solutions of second order elements are better accurate and improved than those of linear elements. Results obtained by the developed model and RMA-2 model are compared, and the results for the developed model were better accurate than those of RMA-2 model. In the future if the developed model is applied in natural rivers, it can provide better accurate results than those of existing model.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2006.05a
• /
• pp.425-429
• /
• 2006

The understanding and prediction of the behavior of flow in open channels are important to the solution of a wide variety of practical flow problems in water resources engineering. Recently, frequent drought has increased the necessity of an effective water resources control and management of river flows for reserving instream flow. The objective of this study is to develop an efficient and accurate finite element model based on Streamline Upwind/Petrov-Galerkin(SU/PG) scheme for analyzing and predicting two dimensional flow features in complex natural rivers. Several tests were performed in developed all elements(4-Node, 6-Node, 8-Node elements) for the purpose of validation and verification of the developed model. The U-shaped channel of flow and natural river of flow were performed for tests. The results were compared with these of laboratory experiments and RMA-2 model. Such results showed that solutions of high order elements were better accurate and improved than those of linear elements. Also, the suggested model displayed reasonable velocity distribution compare to RMA-2 model in meandering domain for application of natural river flow. Accordingly, the developed finite element model is feasible and produces reliable results for simulation of two dimensional natural river flow. Also, One contribution of this study is to present that results can lead to significant gain in analyzing the accurate flow behavior associated with hydraulic structure such as weir and water intake station and flow of chute and pool.

• Korea-Australia Rheology Journal
• /
• v.16 no.3
• /
• pp.117-128
• /
• 2004

The effect of molecular parameters on the steady vortex behaviors in the inertial viscoelastic flow past a cylinder has been investigated. FENE-CR model was considered as a constitutive equation. A recently developed iterative solution method (Kim et al., (in press)) was found to be successfully applicable to the computation of inertial viscoelastic flows. The high-resolution computations were carried out to understand the detailed flow behaviors based on the efficient iterative solution method armed with ILU(0) type pre-conditioner and BiCGSTAB method. The discrete elastic viscous split stress-G/streamline upwind Petrov Galerkin (DEVSS-G/SUPG) formulation was adopted as a stabilization method. The vortex size decreased as elasticity increases. However, the vortex enhancement was also observed in the case of large extensibility, which means that the vortex behavior is strongly dependent upon the material parameters. The longitudinal gradient of normal stress was found to retard the formation of vortex, whereas the extensional viscosity played a role in the vortex enhancement. The present results are expected to be helpful for understanding the inertial vortex dynamics of viscoelastic fluids in the flow past a confined cylinder.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.23 no.1
• /
• pp.43-57
• /
• 1999

The fluid flow and heat transfer in a thin liquid film are investigated numerically. The flow Is assumed to be two-dimensional laminar and surface tension is considered. The most important characteristics of this flow is the existence of a hydraulic jump through which the flow undergoes very sharp and discontinuous change. Arbitrary Lagrangian-Eulerian(ALE) method is used to describe moving free boundary and a modified SIMPLE algorithm based on streamline upwind Petrov-Galerkin(SUPG) finite element method is used for time marching iterative solution. The numerical results obtained by solving unsteady full Navier-Stokes equations are presented for planar and radial flows subject to constant wall temperature or constant wall heat flux, and compared with available experimental data. It Is discussed systematically how the inlet Reynolds and Froude numbers and surface tension affect the formation of a hydraulic jump. In particular, the effect of temperature dependent fluid properties is also discussed.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.24 no.12
• /
• pp.1555-1569
• /
• 2000

Numerical simulation of fluid flow with moving free surface has been carried out. For the free surface flow, a VOF(Volume of Fluid)-based algorithm utilizing a fixed grid system has been investigated. In order to reduce numerical smearing at the free surface represented on a fixed grid system, a new free surface tracking algorithm based on the donor-acceptor scheme has been presented. Novel features of the proposed algorithm are characterized as two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby-cell to determine the fluid volume flux at each cell boundary. The proposed algorithm can be easily implemented in any irregular non-uniform grid systems that are usual in finite element method (FEM). Moreover, the proposed algorithm can be extended and applied to the 3-D free surface flow problem without additional efforts. For computation of unsteady incompressible flow, a finite element approximation based on the explicit fractional step method has been adopted. In addition, the SUPG(streamline upwind/Petrov-Galerkin) method has been implemented to deal with convection dominated flows. Combination of the proposed free surface tracking scheme and explicit fractional step formulation resulted in an efficient solution algorithm. Validity of the present solution algorithm was demonstrated from its application to the broken dam and the solitary wave propagation problems.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.31 no.6B
• /
• pp.507-514
• /
• 2011

A numerical model has been developed by employing a finite element method to simulate the depth-averaged 2-D dispersion of the heat pollutant, which is an important pollutant material in natural streams. Among the finite element methods, the Streamline Upwind/Petrov Galerkin (SUPG) method was applied. Also both linear and quadratic elements can be applied so that irregular river boundaries can be easily represented. To show the movement of heat pollutants, the reaction term describing heat transfer was represented as an equation in which sink/source term is proportional to the difference between the equilibrium temperature and water surface temperature. The equation was expressed so that the water surface temperature changes according to the temperature transfer coefficient and the equilibrium temperature. For the calibration of the model developed, analytic and numerical results from a case of rectangular channel with full width continuous injection have been compared in a steady state. The comparisons showed that the numerical results were in good agreement with analytical solutions. The application site was selected from the downstream of Paldang dam to Jamsil submerged weir, and overall length of this site is about 22.5 km. The change of water temperature caused by the discharge from the Guri sewage treatment plant has been simulated, and results were similar to the observed data. Overall it is concluded that the developed model can represent the water temperature changes due to heat transport accurately. But the verification using observed data will further enhance the validity of the model.