• 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.

• 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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.33 no.1
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• pp.17-23
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• 2020

In this study, the behaviors of a vessel and the ground during the vessel impacting an underwater slope that is part of an artificial protective island are analyzed using the coupled Eulerian-Lagrangian scheme. To consider the large deformation including the shear failure of soil, the Eulerian domain is used to model the ground and water, while the impacting objects are modeled as the Lagrangian domain. For efficiency, the mass scaling scheme is applied to the modeling of the impacting objects, and the ground is modeled by setting the Eulerian volume fraction values. To verify the applicability of the constructed model, a dynamic penetration anchor problem is analyzed. The impacting vessel is modeled using solid elements following the external shape of a container ship, and an analysis of a collision on the slope is performed. As a result, collision behaviors such as displacement, velocity, and dissipation energy are estimated, and the necessity of a parametric study as further research is established.

• 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.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2006.05a
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• pp.99-104
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• 2006

A semi-Lagrangian finite element scheme with objective time stepping algorithm for solving viscoelastic flow problem is presented. The convection terms in the momentum and constitutive equations are treated using a quasi-monotone semi-Lagrangian scheme, in which characteristic feet on a regular grid are traced backwards over a single time-step. Concerned with the generalized midpoint rule type of algorithms formulated to exactly preserve objectivity, we use the geometric transformation such as pull-back, push-forward operation. The method is applied to the 4:1 planar contraction problem for an Oldroyd B fluid for both creeping and inertial flow conditions.

• 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 Korea Water Resources Association
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• v.32 no.2
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• pp.99-110
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• 1999

The method of moments, a Lagrangian scheme, considers the zeroth, first, and second moments of the grid cell spatial distributions of the concentration and then advects the concentration by maintaining conservation of the moments. The reasonable inital description of the first and second moments as well as the mean concentration, the zeroth moments, in grid element is important in the method of moments. In this study, the description methods of each initial moment are reviewed, and the method of moments is extended to overcome the restrictions of Courant number. Its performance is compared with those of available Eulerian and Lagrangian schemes. As the results, the method is successfully extended to overcome the stability restriction and is an accurate scheme for the advection simulation of concentration distribution, especially of which the gradient is steep. In addition, the method is very promising scheme in terms of computational efficiency when the mixing is confined in a relatively small region to the entire domain in two-dimensional problem.

• Applied Science and Convergence Technology
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• v.27 no.1
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• pp.14-18
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• 2018

In order to understand the mechanism of the synthesis of particles using a plasma torch, it is necessary to understand the reaction mechanisms using a computer simulation. In this study, we have developed a simulation method to combine the Lagrangian scheme to follow microparticles and a nodal method to treat nanoparticles categorized with different particle sizes. The Lagrangian scheme includes the Coulomb force which affects the dynamics of larger particles. In contrast, the nodal method is adequate for the nanoparticles because the charge effect is negligible for nanoparticles but the number of nanoparticles is much larger than that of microparticles. This method is helpful to understand the dynamics and growth mechanism of micro- and nano-powder mixture observed in the experiment.

• Journal of the Korea Institute of Military Science and Technology
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• v.13 no.3
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• pp.349-357
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• 2010

In this paper, a numerical code for the interior ballistics has been investigated. The Eulerian-Lagrangian approach and the SMART scheme have been used in the numerical code for the grain combustion. The translational kinetic energy of the projectile and work done against barrel friction have been considered only. The ghost cell extrapolation method has been used for the chamber change with the projectile movement. The calculation results of the numerical code have been compared and verified through those of IBHVG2 code.

• East Asian mathematical journal
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• v.35 no.1
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• pp.59-66
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• 2019

In this paper we study implicit-explicit (IMEX) methods combined with a semi-Lagrangian scheme to evaluate the prices of fixed strike arithmetic Asian options under jump-diffusion models. An Asian option is described by a two-dimensional partial integro-differential equation (PIDE) that has no diffusion term in the arithmetic average direction. The IMEX methods with the semi-Lagrangian scheme to solve the PIDE are discretized along characteristic curves and performed without any fixed point iteration techniques at each time step. We implement numerical simulations for the prices of a European fixed strike arithmetic Asian put option under the Merton model to demonstrate the second-order convergence rate.