• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.4
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• pp.315-322
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• 2009

This paper presents a novel numerical method based on the extended moving least squares finite difference method(MLS FDM) for solving 1-D Stefan problem. The MLS FDM is employed for easy numerical modelling of the moving boundary and Taylor polynomial is extended using wedge function for accurate capturing of interfacial singularity. Difference equations for the governing equations are constructed by implicit method which makes the numerical method stable. Numerical experiments prove that the extended MLS FDM show high accuracy and efficiency in solving semi-infinite melting, cylindrical solidification problems with moving interfacial boundary.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.86-87
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• 2003

Unstructured grid system is suitable for flows of complex geometries. For problems with moving boundary walls, the grid system must be changed and deformed with time if we use a body fitted grid system. In this paper, a new moving-grid finite-volume method on unstructured grid system is proposed and developed for unsteady compressible flows with shock waves. To assure geometric conservation laws on moving grid system, a control volume on the space-time unified domain is adopted for estimating numerical flux. The method is described and applied for two-dimensional flows.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.6
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• pp.619-627
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• 2004

In most industrial applications, the geometrical complexity is combined with the moving boundaries. These problems considerably increase the computational difficulties since they require, respectively, regeneration and deformation of the grid. As a result, engineering flow simulation is restricted. In order to solve this kind of problems the immersed boundary method was developed. In this study, the immersed boundary method is applied to the numerical simulation of stationary, rotating and oscillating cylinders in the 2-dimensional square cavity. No-slip velocity boundary conditions are given by imposing feedback forcing term to the momentum equation. Besides, this technique is used with a second-order accurate interpolation scheme in order to improve the accuracy of flow near the immersed boundaries. The governing equations for the mass and momentum using the immersed boundary method are discretized on the non-staggered grid by using the finite volume method. The results agree well with previous numerical and experimental results. This study presents the possibility of the immersed boundary method to apply to the complex flow experienced in the industrial applications. The usefulness of this method will be confirmed when we solve the complex geometries and moving bodies.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.8
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• pp.670-676
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• 2007

A comparative study on ground boundary conditions for the airfoil in ground effect has been carried out. The objective of the present study is to clarify effects of the ground boundary conditions so that it will be helpful to analyse results of wind tunnel tests using the fixed ground board or the image method. A low Mach number preconditioned Navier-Stokes solver using the overlap grid method has been applied. It has been turned out that results with the symmetric boundary condition are almost the same to those with the moving boundary condition. Results with the fixed ground boundary show discrepancy to those with the moving boundary condition when flow separation on the ground board takes place.

• Structural Engineering and Mechanics
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• v.86 no.3
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• pp.361-371
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• 2023

Boundary condition is an important factor affecting the vibration characteristics of structures, under different boundary conditions, structures will exhibit different vibration behaviors. On the basis of the previous work, this paper extends to the nonlinear resonance behavior of axially moving graphene platelets reinforced metal foams (GPLRMF) plates with geometric imperfection under different boundary conditions. Based on nonlinear Kirchhoff plate theory, the motion equations are derived. Considering three boundary conditions, including four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS), the nonlinear ordinary differential equation system is obtained by Galerkin method, and then the equation system is solved to obtain the nonlinear ordinary differential control equation which only including transverse displacement. Subsequently, the resonance response of GPLRMF plates is obtained by perturbation method. Finally, the effects of different boundary conditions, material properties (including the GPLs patterns, foams distribution, porosity coefficient and GPLs weight fraction), geometric imperfection, and axial velocity on the resonance of GPLRMF plates are investigated.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.5
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• pp.439-446
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• 2012

This paper presents an implicit moving least squares(MLS) difference method for improving the solution accuracy of 1-D free boundary problems, which implicitly updates the topology change of moving interface. The conventional MLS difference method explicitly updates the moving interface; it requires no iterative solution procedure but results in the loss of accuracy. However, the newly developed implicit scheme makes the total system nonlinear involving iterative solution procedure, but numerical verification show that it dramatically elevates the solution accuracy with moderate computation increase. Through numerical experiments for melting problems having moving singularity, it is verified that the proposed method can achieve the second order accuracy.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.342-347
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• 2003

In this paper, an active vibration control of a translating tensioned string with the use of an electro-hydraulic servo mechanism at the right boundary is investigated. The dynamics of the moving strip is modeled as a string with tension by using Hamilton’s principle for the systems with changing mass. The control objective is to suppress the transverse vibrations of the strip via boundary control. A right boundary control law in the form of current input to the servo valve based upon the Lyapunov’s second method is derived. It is revealed that a time-varying boundary force and a suitable passive damping at the right boundary can successfully suppress the transverse vibrations. The exponential stability of the closed loop system is proved. The effectiveness of the control laws proposed is demonstrated via simulations.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.1
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• pp.39-48
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• 2013

This paper develops a 2-D moving least squares(MLS) difference method for Stefan problem by extending the 1-D version of the conventional method. Unlike to 1-D interfacial modeling, the complex topology change in 2-D domain due to arbitrarily moving boundary is successfully modelled. The MLS derivative approximation that drives the kinetics of moving boundary is derived while the strong merit of MLS Difference Method that utilizes only nodal computation is effectively conserved. The governing equations are differentiated by an implicit scheme for achieving numerical stability and the moving boundary is updated by an explicit scheme for maximizing numerical efficiency. Numerical experiments prove that the MLS Difference Method shows very good accuracy and efficiency in solving complex 2-D Stefan problems.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2007.11a
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• pp.229-232
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• 2007

A numerical method for the moving boundary required in analysis of the combustion phenomenon of the solid propellant has been studied. The ghost cell extrapolation has been used in the Eulerian coordinate system. The Lagrangian method has been used in Non-Eulerian coordinate system. Results of the numerical analysis were verified by comparing to theoretical results of 1-D free-moving piston in the pipe.

• Interaction and multiscale mechanics
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• v.2 no.4
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• pp.333-352
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• 2009

We introduce a radial basis collocation method to solve axially moving beam problems which involve $2^{nd}$ order differentiation in time and $4^{th}$ order differentiation in space. The discrete equation is constructed based on the strong form of the governing equation. The employment of multiquadrics radial basis function allows approximation of higher order derivatives in the strong form. Unlike the other approximation functions used in the meshfree methods, such as the moving least-squares approximation, $4^{th}$ order derivative of multiquadrics radial basis function is straightforward. We also show that the standard weighted boundary collocation approach for imposition of boundary conditions in static problems yields significant errors in the transient problems. This inaccuracy in dynamic problems can be corrected by a statically condensed semi-discrete equation resulting from an exact imposition of boundary conditions. The effectiveness of this approach is examined in the numerical examples.