• 한국전산유체공학회:학술대회논문집
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• 2002.10a
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• pp.47-52
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• 2002

We present an improved Lagrangian vortex method in 2-D incompressible unsteady viscous flows, which is based on a mesh-free integral approach of the velocity-vorticity formulation. Vorticity fields are represented by discrete vortex blobs that are updated by the Lagrangian vorticity transport with the particle strength exchange scheme. Velocity fields are expressed in a form of the Helmholtz decomposition, which are calculated by a fast algorithm of the Biot-Savart integration with a smoothed kernel and by a well-established panel method. No-slip condition is enforced through viscous diffusion of vorticity from a solid body into field. The vorticity flux is determined in such a way that spurious slip velocity vanishes. Through the comparison with the existing finite volume scheme for the transient vortical flows around an impulsively started cylinder at Reynolds number Re=550, we would obtain a more accurate scheme for vortex methods in complicated flows.

• 한국전산유체공학회:학술대회논문집
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• 2003.08a
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• pp.43-48
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• 2003

When the Eulerian-Lagrangian method is used to analyze the particle laden two-phase flow, a large number of particles should be used to obtain statistically meaningful solutions. Then it takes too much time to track the particles and to average the particle properties in the numerical analysis of two-phase flow. The purpose of this paper is to reduce the computation time by means of a set of particle gird separate to the flow grid. Particle motion equation here is the simplified B-B-O equation, which is integrated to get the particle trajectories. Particle turbulent dispersion, wall collision, and wall roughness effects are considered but the two-way coupling effects between gas and particles are neglected. Particle laden 2-D channel flow is solved and it is shown that the computational efficiency is indeed improved by using the current method

• Proceedings of the KIEE Conference
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• 1996.11a
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• pp.133-136
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• 1996

In the paper, an artificial neural network (ANN) approach based on Lagrange multiplier method (Lagrangian ANN) is used to solve an economic load dispatch (ELD) problem. Traditionally ELD problem has one convex cost function as its objective function and nonlinear constraints such as power balance and maximum-minimum limits of real power. In this study, modification is given to the Lagrangian ANN proposed by Gong et all[5] to guarantee the convergence to the optimal solution. Simulation results demonstrate the effectiveness of the proposed method applied to the ELD problem.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.569-583
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• 2019

Given a graph G, the Motzkin and Straus formulation of the maximum clique problem is the quadratic program (QP) formed from the adjacent matrix of the graph G over the standard simplex. It is well-known that the global optimum value of this QP (called Lagrangian) corresponds to the clique number of a graph. It is useful in practice if similar results hold for hypergraphs. In this paper, we attempt to explore the relationship between the Lagrangian of a hypergraph and the order of its maximum cliques when the number of edges is in a certain range. Specifically, we obtain upper bounds for the Lagrangian of a hypergraph when the number of edges is in a certain range. These results further support a conjecture introduced by Y. Peng and C. Zhao (2012) and extend a result of J. Talbot (2002). We also establish an upper bound of the clique number in terms of Lagrangians for hypergraphs.

• Journal of the Korean Physical Society
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• v.73 no.12
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• pp.1840-1844
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• 2018

Working in an arbitrary Lorentz frame, we address the question of formulating the covariant variational principle for classical, single-particle, dissipative, relativistic mechanics. First, within a Minkowskian geometry, the basic properties of the proper time ${\tau}$ and the covariant velocity $u_{\mu}$ are recapitulated. Next, using a scalar function ${\psi}(x)$ and its negative derivatives ${\varphi}_{\mu}{^{\prime}}s$, we construct a covariant Lagrangian ${\Lambda}$ that generalizes the famous Bateman-Caldirola-Kanai Lagrangian of nonrelativistic frictional mechanics. Finally, we propose a deterministic model for ${\psi}$ (involving the drag coefficient A) whose explicit solution leads to relativistic damped Rayleigh motion in the rest frame of the medium.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.3 s.73
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• pp.223-231
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• 2006

This study deals with behavior characteristics of laminated composite folded structures according to ratio of folded length based on a higher-order shear deformation theory. Well-known mixed finite element method using Lagrangian and Hermite shape interpolation functions is a little complex and have some difficulties applying to a triangular element. However, a higher-order shear deformation theory using only Lagrangian shape interpolation functions avoids those problems. In this paper, a drilling degree of freedom is appended for more accurate analysis and computational simplicity of folded plates. There are ten degrees of freedom per node, and four nodes per element. Journal on folded plates for effects of length variations is not expressed. Many results in this study are carried out according to ratio of folded length. The rational design is possible through analyses of complex and unpredictable laminated composite folded structures.

• Transactions of the Korean Society of Automotive Engineers
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• v.20 no.1
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• pp.39-45
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• 2012

In the standard CFD code, Lagrangian-Eulerian method is very popular to simulate the liquid spray penetrating into gaseous phase. Though this method can give a simple solution and low computational cost, it have been reported that the Lagrangian spray models have numerical grid dependency, resulting in serious numerical errors. Many researches have shown the grid dependency arise from two sources. The first is due to unaccurate prediction of the droplet-gas relative velocity, and the second is that the probability of binary droplet collision is dependent on the grid resolution. In order to solve the grid dependency problem, the improved spray models are implemented in the KIVA-3V code in this study. For reducing the errors in predicting the relative velocity, the momentum gain from the gaseous phase to liquid particles were resolved according to the gas-jet theory. In addition, the advanced algorithm of the droplet collision modeling which surmounts the grid dependency problem was applied. Then, in order to validate the improved spray model, the computation is compared to the experimental results. By simultaneously regarding the momentum coupling and the droplet collision modeling, successful reduction of the numerical grid dependency could be accomplished in the simulation of the high-pressure injection diesel spray.

• Water for future
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• v.28 no.4
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• pp.125-136
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• 1995

ELM, a characteristic line based method, was applied to advection-dispersion equation, and the results obtained were compared with those of Eulerian schemes(Stone-Brian and QUICKEST). The calculation methods consisted of Lagrangian interpolation scheme and cubic spline interpolation scheme for the advection calculation, and the Crank-Nicholson scheme for the dispersion calculation. The results of numerical methods were as follows: (1) for Gaussian hill: ELM, using Lagrangian interpolation scheme, gave the most accurate computational result, ELM, using cubic spline interpolation scheme, and QUICKEST scheme gave numerical damping for Peclet number 50. Stone-Brian scheme gave phase shift introduced in the numerical solution for Peclet number 10 and 50. (2) for advanced front: All schemes gave accurate computational results for Peclet number 1 and 4. ELM, Lagrangian interpolation scheme, and Stone,Brian scheme gave dissipation error and ELM, using cubic spline interpolation scheme, and QUICKEST scheme gave numerical oscillation for Peclet number 50.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.21 no.2
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• pp.108-116
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• 2009

The present study introduces a Legendre interpolation function which is capable of analyzing wave transformation effectively in a finite element method. A Lagrangian interpolation function has been mostly used for a finite element method with a higher-order interpolation function. Although this function has an advantage of giving an accurate result with less number of elements, simulation time increases. Calculation time can be reduced by mass lumping, whereas the accuracy of solution is lowered. In this study, we introduce a modified Lagrangian interpolation function, Legendre cardinal interpolation, which can reduce simulation time with keeping up favorable accuracy. Through various numerical simulations using a Boussinesq equations model, the superiority of the Legendre cardinal interpolation function to a Lagrangian interpolation function was shown.

• Journal of the Korean GEO-environmental Society
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• v.4 no.1
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• pp.5-10
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• 2003

The solids and the fluids in porous media have a relative velocity to each other. Due to physically and chemically different material properties and their relative velocity, the behavior of saturated porous media is extremely complicated. Thus, in order to describe and clarify the deformation behavior of saturated porous media, constitutive models for deformation of porous media coupling several effects need to be developed in frame of Arbitrary Lagrangian Eulerian(ALE) description. The aim of ALE formulations is to maximize the advantages of Lagrangian and Eulerian elements, and to minimize the disadvantages. Therefore, this method is appropriate for the analysis of porous media which are considered for the behavior of the solids and the fluids. For this reason, mass balance equations for saturated porous media are derived here in ALE description frames. ALE formulations of mass conservation for the solid phase and the fluid phase are expressed. Then, linear momentum balance equation for porous media as multiphase media is expressed.