• Journal of the Society of Naval Architects of Korea
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• v.41 no.1
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• pp.23-30
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• 2004

In the Lagrangian vortex particle method based on the vorticity-velocity formulation for solving the incompressible Navier-Stokes equations, a numerical scheme for calculating pressure fields is presented. Implementation of the numerical method is directly connected with the well-established surface panel methods, just by dealing with the dynamic coupling among vorticity field. Assuming the vorticity and the velocity fields are to be calculated in time domain analysis, the pressure calculation for a complete set of solution at present time step is performed in a similar way to the one used in the Eulerian description. For a validation of the present method, we illustrate the early development of the viscous flow about an impulsive started circular cylinder for Reynolds number 550. The comparative study with the Eulerian finite Volume method provides an extensive understanding and application of the mesh-free Lagrangian vortex methods for numerical simulation of viscous flows around arbitrary bodies of general shape.

• Journal of computational fluids engineering
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• v.6 no.3
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• pp.19-26
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• 2001

An Eulerian-Lagrangian method, so called immersed boundary method, is used for analysing viscous flow around arbitrary bodies, where governing equations are discretized on a regular grid by using a finite volume method. To improve the accuracy of flow near body boundaries, a second-order accurate interpolation scheme is used and a level-set based grid deformation method is presented to construct the adaptive grids around body boundaries. The present scheme is used to simulate steady flow around a semicircular cylinder mounted on the bottom of flow domain and calculated results are validated by results of a body fitted grid method. Finally, present method is applied to a complex flow around multi body and the usefulness is checked by investigating calculated results.

• Journal of computational fluids engineering
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• v.9 no.3
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• pp.8-17
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• 2004

A Semi-Lagrangian method based on CIP(Cubic Interpolated Pseudoparticle)method is proposed and it is applied to solve the two dimensional advection equation. Especially the attentions are given to settle the pole problem and to enhance the accuracy in solving the advection equation on the spherical coordinate system. Tn this algorithm, the CU method is employed as the Semi-Lagrangian method and extended to the spherical coordinate system. To enhance the accuracy of the solution, the spatial discretization is made by CIP method. The mathematical formulation and numerical results are also described. To verify the efficiency, accuracy and capability of proposed algorithm, two dimensional rotating cosine bell problem and the frontogenesis problem are simulated by the present scheme. As results, it is confirmed that the present scheme gives an accurate solution and settles the pole problem in the advection equation on the sphere.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.6
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• pp.755-760
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• 2010

In general, Lagrangian method for discrete optimization is a kind of technique to easily manage constraints. It is traditionally used for finding upper bounds in the branch-and-bound method. In this paper, we propose a new Lagrangian search method for the 0-1 knapsack problem with multiple constraints. A novel feature of the proposed method different from existing Lagrangian approaches is that it can find high-quality lower bounds, i.e., feasible solutions, efficiently based on a new property of Lagrangian vector. We show the performance improvement of the proposed Lagrangian method over existing ones through experiments on well-known large scale benchmark data.

• Nuclear Engineering and Technology
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• v.55 no.12
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• pp.4395-4407
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• 2023

Bubble columns are widely encountered in several industries, especially in the field of nuclear safety. The Eulerian-Eulerian and the Eulerian-Lagrangian methods are commonly used to investigate bubble columns. Eulerian approaches require additional tasks such as strict volume conservation at the interface and a predefined well-structured grid. In contrast, the Lagrangian approach can be easily implemented. Hence, we introduce a fully Lagrangian approach for the simulation of bubble columns using the discrete bubble model (DBM) and moving particle semi-implicit (MPS) methods. Additionally, we propose a rigorous method to estimate the volume fraction accurately, and verified it through experimental data and analytical results. The MPS method was compared with the experimental data of Dambreak. The DBM was verified by analyzing the terminal velocity of a single bubble for each bubble size. It agreed with the analytical results for each of the four drag correlations. Additionally, the improved method for calculating the volume fraction showed agreement with the Ergun equation for the pressure drop in a packed bed. The implemented MPS-DBM was used to simulate the bubble column, and the results were compared with the experimental results. We demonstrated that the MPS-DBM was in quantitative agreement with the experimental data.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.381-388
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• 2006

A porous medium is composed of solids, fluids, and gas which have different physical and chemical properties. In addition, these constituents have a relative velocity between each other. So far, in order to analyze porous media using finite element method, Lagrangian or Eulerian method has been used. However, the numerical analyses for porous media have a defect that the methods do not describe the movements of constituents. In this paper, numerical analysis for unsaturated porous media was performed in frame of ALE method which has advantages of Lagrangian and Eulerian. Namely, the Lagrangian description was used in solid phase, and the Eulerian description was used in fluid or gas phase in a porous medium Then the relationship between each other was controlled by the convective term in ALE method. Finally, the numerical results of ALE were compared with tile results of Lagrangian analysis.

• 한국전산유체공학회:학술대회논문집
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• 2003.08a
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• pp.37-42
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• 2003

A vorticity-velocity integro-differential formulation of incompressible Wavier-Stokes equations is described, focusing on a scheme for calculating pressure fields in application of the Lagrangian vortex method in connection with panel methods. It deals with the dynamic coupling among velocity, vorticity and pressure, and the Helmholtz decomposition of the velocity field, through a comparative study with the Eulerian finite volume method, we provide an extensive understanding of the Lagrangian vortex methods for numerical simulations of viscous flows around arbitrary bodies.

• Journal of Electrical Engineering and Technology
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• v.3 no.4
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• pp.514-519
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• 2008

The non-separable quadratic penalty terms create an inherent difficulty when applying the standard augmented Lagrangian relaxation(ALR) method for decomposing the unit commitment problem into independent subproblems. This paper presents a separable augmented Lagrangian relaxation method for solving the unit commitment problem. The proposed method is designed to have a separable structure by introducing the quadratic terms with additional auxiliary terms in the augmented Lagrangian function. Numerical results are presented to validate the effectiveness of the proposed method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.1-15
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• 2002

Advection-dominated transport problems possess difficulties in the design of numerical methods for solving them. Because of the hyperbolic nature of advective transport, many characteristic numerical methods have been developed such as the classical characteristic method, the Eulerian-Lagrangian method, the transport diffusion method, the modified method of characteristics, the operator splitting method, the Eulerian-Lagrangian localized adjoint method, the characteristic mixed method, and the Eulerian-Lagrangian mixed discontinuous method. In this paper relationships among these characteristic methods are examined. In particular, we show that these sometimes diverse methods can be given a unified formulation. This paper focuses on characteristic finite element methods. Similar examination can be presented for characteristic finite difference methods.

• Journal of Soil and Groundwater Environment
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• v.11 no.1
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• pp.37-44
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• 2006

This study summarizes advantages and disadvantages of numerical methods and compares ELLAM and LEZOOMPC to develop an efficient numerical modeling technique on contaminant transport. Eulerian-Lagrangian method and Eulerian method are commonly used numerical techniques. However Eulerian-Lagrangian method does not conserve mass globally and fails to treat boundary in a straightforward manner. Also, Eulerian method has restrictions on the size of Courant number and mesh Peclet number because of time truncation error. ELLAM (Eulerian Lagrangian Localized Adjoint Method) which has been popularly used for past 10 years in numerical modeling, is known for overcoming these numerical problems of Eulerian-Lagrangian method and Eulerian method. However, this study investigates advantages and disadvantages of ELLAM and suggests a change for the better. To figure out the disadvantages of ELLAM, the results of ELLAM, LEZOOMPC (Lagrangian-Eulerian ZOOMing Peak and valley Capturing), and visual MODFLOW are compared for four examples having different mesh Peclet numbers. The result of ELLAM generates numerical oscillation at infinite of mesh Peclet number, but that of LEZOOMPC yields accurate simulations. The simulation results suggest that the numerical error of ELLAM could be alleviated by adopting some schemes in LEZOOMPC. In other words, the numerical model which combines ELLAM with backward particle tracking, forward particle tracking, adaptively local zooming, and peak/valley capturing of LEZOOMPC can be developed for not only overcoming the numerical error of ELLAM, but also keeping the numerical advantage of ELLAM.