• 한국지구물리탐사학회:학술대회논문집
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• 2008.10a
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• pp.57-62
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• 2008

Finite difference method using not general SSG(standard staggered grid) but RSG(rotated staggered grid) was applied to simulation of elastic wave propagation. Special free surface boundary condition such as imaging method is needed in finite difference method using SSG in elastic wave propagation but free surface boundary condition in finite difference method using RSG is easily solved with adding air layer. Recently PML(Perfectly Matched layer) is widely used to eliminate artificial reflection waves from finite boundary because of its' greate efficiency. Absorbing ability of CPML(convolutional Perfectly Matched Layer) that is more efficient than that of PML was applied to FDM using RSG in this study. The results of CPML eliminated artificial boundary waves very effectively in FDM using RSG in being compared with that of Cerjan's absorbing method.

• Journal of computational fluids engineering
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• v.7 no.1
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• pp.10-19
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• 2002

The non-staggered(collocated) grid approach in which all the solution variables are located at the centers of control volumes is very popular for incompressible flow analyses because of its numerical efficiency on the curvilinear or unstructured grids. Rhie and Chow's paper is the first in using non-staggered grid method for SIMPLE algorithm, where pressure weighted interpolation was used to prevent decoupling of pressure and velocity. But it has been known that this non-staggered grid method has stability problems when pressure fields are nonlinear like in natural convection flows. Also Rhie-Chow scheme generates large numerical diffusion near curved walls. The cause of these unwanted problems is too large pressure damping term compared to the magnitude of face velocity. In this study the magnitude of pressure damping term of Rhie-Chow's method is limited to 1∼10% of face velocity to prevent physically unreasonable solutions. The wall pressure extrapolation which is necessary for cell-centered FVM is another source of numerical errors. Some methods are applied in a unstructured FV solver and analyzed in view of numerical accuracy. Here, two natural convection problems are solved to check the effect of the Rhie-Chow's method on numerical stability. And numerical diffusion from Rhie-Chow's method is studied by solving the inviscid flow around a circular cylinder.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1821-1826
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• 2003

In this study, we discuss CIP method, which can treat compressible/incompressible problem and multi-phase problem. We can apply this method to the general equations by using CCUP. In this paper, non-staggered grid arrangement and predictor-corrector method are used to enhance later development and the solution accuracy and convergence performance. To validate the numerical algorithm proposed in this paper, the two-dimensional unsteady flow in the driven cavity is simulated. The numerical results of this subject using the present algorithm are compared with other numerical results. As a result, it is prived that the present scheme gives stable and improved solutions, and the results even coarse grid are in good agreement with other result using a fine grid arrangement.

• Geophysics and Geophysical Exploration
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• v.12 no.2
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• pp.183-191
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• 2009

Finite difference method using not general SSG (standard staggered grid) but RSG (rotated staggered grid) was applied to simulation of elastic wave propagation. Special free surface boundary condition such as imaging method is needed in finite difference method using SSG in elastic wave propagation. But free surface boundary condition in finite difference method using RSG is easily solved with adding air layer or vacuum layer. Recently PML (Perfectly Matched layer) is widely used to eliminate artificial reflection waves from finite boundary because of its' greate efficiency. Absorbing ability of CPML (convolutional Perfectly Matched Layer) that is more efficient than that of PML and CPML that don't use splitting of wave equation that should be adapted to PML was applied to FDM using RSG in this study. Frequency absorbing characteristic and energy absorbing ability in CPML layer were investigated and CPML eliminated artificial boundary waves very effectively in FDM using RSG in being compared with that of Cerjan's absorbing method. CPML method also diminished amplitude of waves in boundary layer of solid-liquid model very well.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.67-82
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• 2006

In this paper, we present a finite difference method for the implementation of the rotation of a circular cylinder in the incompressible flow field by solving the two-dimensional unsteady Navier-Stokes equations. The approach is to use staggered grid method so that the accuracy and order of convergence of the associated algorithms can be maintained. The proposed method is easy to be implemented and is effective. A set of simulations for the flow dynamics is provided to show the computational results.

• Journal of computational fluids engineering
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• v.12 no.1
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• pp.1-8
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• 2007

A code is developed using the hybrid Cartesian/immersed boundary method and it is applied to simulate flows around a three-dimensional deforming body. A new criterion is suggested to distribute the immersed boundary nodes based on edges crossing a body boundary. Velocities are reconstructed at the immersed boundary nodes using the interpolation along a local normal line to the boundary. Reconstruction of the pressure at the immersed boundary node is avoided using the hybrid staggered/non-staggered grid method. The developed code is validated through comparisons with other experimental and numerical results for the velocity profiles around a circular cylinder under the forced in-line oscillation and the pressure coefficient distribution on a sphere. The code is applied to simulate the flow fields around a plate whose tail is periodically flapping under a translation. The effects of the velocity and acceleration due to the deformation on the periodic shedding of pairs of tip vortices are investigated.

• Journal of computational fluids engineering
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• v.12 no.2
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• pp.37-45
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• 2007

The hybrid Cartesian/immersed boundary method is applied to simulate fluid-structure interaction of a two-dimensional orbiting flexible foil. The elastic deformation of the flexible foil is modelled based on the dynamic equation of a thin-plate. At each time step, the locations and velocities of the Lagrangian control points on the flexible foil are used to reconstruct the boundary conditions for the flow solver based on the hybrid staggered/non-staggered grid. To test the developed code, the flow fields around a flapping elliptical wing are calculated. The time history of the vertical force component and the evolution of the vorticity fields are compared with recent other computations and good agreement is achieved. For the orbiting flexible foil, the vorticity fields are compared with those of the case without the deformation. The combined effects of the angle of attack and the orbit on the deformation are investigated. The grid independency study is carried out for the computed time history of the deformation at the tip.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.96-101
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• 1998

Various discretiation methods of Laplacian operator in the Pressure-Poisson equation are investigated for the solution of incompressible Navier-Stokes equations using the non-staggered grid. Laplacian operators previously proposed by other researchers are applied to a Driven-Cavity problem. The computational results are compared with those of Ghia. The results show the characteristics of the discrete Laplacian operators.

• Journal of the Korean earth science society
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• v.39 no.4
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• pp.317-326
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• 2018

Effect of the nonuniform grid on the two-dimensional transport equation was investigated in terms of theoretical analysis and finite difference method (FDM). The nonuniform grid having a typical structure of the numerical weather forecast model was incorporated in the vertical direction, while the uniform grid was used in the zonal direction. The staggered and non-staggered grid were placed in the vertical and zonal direction, respectively. Time stepping was performed with the third-order Runge Kutta scheme. An error analysis of the spatial discretization on the nonuniform grid was carried out, which indicated that the combined effect of the nonuniform grid and advection velocity produced either numerical diffusion or numerical adverse-diffusion. An analytic function is used for the quantitative evaluation of the errors associated with the discretized transport equation. Numerical experiments with the non-uniformity of vertical grid were found to support the analysis.

• Geophysics and Geophysical Exploration
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• v.20 no.3
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• pp.121-128
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• 2017

Interpretation of time-domain electromagnetic (TEM) data has been made mostly based on one-dimensional (1-D) inversion scheme in Korea. A proper interpretation of TEM data should employ 3-D TEM forward and inverse modeling algorithms. This study developed a 3-D TEM modeling algorithm using a finite difference time-domain (FDTD) method with staggered grid. In numerically solving Maxwell equations, fictitious displacement current is included based on an explicit FDTD method using a central difference approximation scheme. The developed modeling algorithm simulated a small-coil source configuration to be verified against analytic solutions for homogeneous half-space models. Further, TEM responses for a 3-D anomaly are modeled and analyzed. We expect that it will contribute greatly to the precise interpretation of TEM data.