• Proceedings of the Computational Structural Engineering Institute Conference
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• 2009.04a
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• pp.308-313
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• 2009

본 논문은 확장된 이동최소제곱 유한차분법을 이용하여 1차원 Stefan 문제를 해석할 수 있는 수치기법이 제시한다. 이동하는 경계의 자유로운 묘사를 위해 요소망이나 그리드 없이 절점만을 사용하는 이동최소제곱 유한차분법을 사용하였으며, 계면경계의 특이성을 모형화하기 위해 Taylor 다항식에 쐐기함수를 도입했다. 지배방정식은 안정성이 높은 음해법(implicit method)을 이용하여 차분하였다. 미분의 특이성을 갖는 이동경계를 포함한 반무한 융해문제의 수치해석을 통해 확장된 이동최소제곱 유한차분법이 높은 정확성과 효율성을 갖는 것을 보였다.

• 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 Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.752-755
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• 2011

이종재료의 열전달문제 수치해석시 추가적으로 만족시켜야 하는 계면경계조건들의 존재와 계면경계로 인한 불연속면의 처리는 근사함수의 구성 뿐만 아니라 수치기법의 개발 자체를 어렵게 만든다. 본 논문에서는 계면경계의 불연속성을 모델링하는 특수한 함수를 포함하고 계면경계조건을 항상 만족시킬 수 있는 근사함수를 구성하고, 계면경계문제의 강형식을 직접 이산화하며 고속으로 해를 계산할 수 있는 이동최소제곱 차분법을 제시한다. 계면경계조건이 매입된 이동최소제곱 차분법으로 이종재료의 열전달문제를 해석한 결과, 높은 정확성과 효율성을 갖는 것을 확인할 수 있었다.

• 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.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2010.04a
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• pp.48-51
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• 2010

본 논문에서는 자유경계문제 해석을 위해 정확도가 향상된 implicit 이동최소제곱 차분법을 제시한다. 계면경계에 대한 implicit 정의로 인해 비선형 시스템이 구성되고, 매 해석단계마다 절점해와 계면경계의 위치를 반복계산을 통해 찾는다. 계면경계 결정시 속도항을 한 단계 뒤로 지연시켜 explicit하게 근사적으로 계산하던 기존 방법에 비해 계면경계의 위치를 더 정확하게 계산할 수 있고, 결과적으로 해의 정확도가 향상되었다. 계면경계 위치값이 비교적 빠른 속도로 수렴하기 때문에 많은 반복계산이 필요치 않다. 수치예제를 통해 기존의 방법으로 계산한 결과와 비교하여 새롭게 개발한 implicit 방법의 향상된 정확도를 보였다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.6
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• pp.779-787
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• 2007

This paper presents a highly efficient moving least squares finite difference method (MLS FDM) for a heat transfer problem of bi-material with interfacial boundary. The MLS FDM directly discretizes governing differential equations based on a node set without a grid structure. In the method, difference equations are constructed by the Taylor polynomial expanded by moving least squares method. The wedge function is designed on the concept of hyperplane function and is embedded in the derivative approximation formula on the moving least squares sense. Thus interfacial singular behavior like normal derivative jump is naturally modeled and the merit of MLS FDM in fast derivative computation is assured. Numerical experiments for heat transfer problem of bi-material with different heat conductivities show that the developed method achieves high efficiency as well as good accuracy in interface problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.5
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• pp.411-420
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• 2009

This study presents an extended finite difference method based on moving least squares(MLS) method for solving potential problems with interfacial boundary. The approximation constructed from the MLS Taylor polynomial is modified by inserting of wedge functions for the interface modeling. Governing equations are node-wisely discretized without involving element or grid; immersion of interfacial condition into the approximation circumvents numerical difficulties owing to geometrical modeling of interface. Interface modeling introduces no additional unknowns in the system of equations but makes the system overdetermined. So, the numbers of unknowns and equations are equalized by the symmetrization of the stiffness matrix. Increase in computational effort is the trade-off for ease of interface modeling. Numerical results clearly show that the developed numerical scheme sharply describes the wedge behavior as well as jumps and efficiently and accurately solves potential problems with interface.

• Journal of Navigation and Port Research
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• v.27 no.5
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• pp.539-546
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• 2003

The numerical model of the flow analysis by finite element technique is described. The Galerkin method is employed for spatial discretization Two step explicit finite element scheme is used to discretize the time function, which has advantage in problems treating large numbers of elements and unsteady state. Two dimensional hydrodynamic model considering moving boundary condition is developed. Also it applied flow model which develop on flow portion of ideal fluid in the model flume and verified, and the results of this study confirm the efficiency of moving boundary treatment in Jeju harbor. The computed results have shown the good adaptability of moving boundary condition From these studies, it can be concluded that the present method is a useful and effective tool in tidal flow analysis.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.10
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• pp.26-34
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• 2005

In this paper, a novel moving least squares interface welding method is proposed to carry out the coupled analysis of whole model composed of independently modeled finite element substructures with nodal mismatching interfaces. To verify the validity, and efficiency of the proposed interface welding method, various numerical examples are worked out including patch tests, convergence tests, and examples of coupled analyses of the structural systems with mismatching substructures. From the numerical tests, it is confirmed that one can efficiently carry out the coupled analysis of whole model composed of mismatching finite element substructures through the proposed method without any remeshing or any additional unknown.