• 한국전산구조공학회논문집
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• 제22권4호
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• pp.315-322
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• 2009

본 논문은 확장된 이동최소제곱 유한차분법을 이용하여 1차원 Stefan 문제를 해석할 수 있는 새로운 수치기법이 제시한다. 이동하는 계면경계의 자유로운 수치적인 묘사를 위해 요소망이나 그리드 없이 절점만을 사용하는 이동최소제곱 유한차분법을 도입하고, 계면경계의 특이성을 모형화하기 위해 Taylor 다항식에 쐐기함수를 도입하여 확장했다. 지배방정식의 차분은 안정성을 보장해 주는 음해법(implicit method)을 이용한다. 이동경계를 포함한 반무한 융해문제, 실린더 형상의 고체화 문제의 수치해석을 통해 확장된 이동최소제곱 유한차분법이 높은 정확성과 효율성을 갖는 것을 보였다.

• 한국주조공학회지
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• 제13권4호
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• pp.323-332
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• 1993

An implicit finite difference formulation with three methods of latent heat treatment, such as equivalent specific heat method, temperature recovery method and enthalpy method, was applied to solidification analysis. The Neumann problem was solved to compare the numerical results with the exact solution. The implicit solutions with the equivalent specific heat method and the temperature recovery method were comparatively consistent with the Neumann exact solution for smaller time steps, but its error increased with increasing time step, especially in predicting the solidification beginning time. Although the computing time to solve energy equation using temperature recovery method was shorter than using enthalpy method, the method of releasing latent heat is not realistic and causes error. The implicit formulation of phase change problem requires enthalpy method to treat the release of latent heat reasonably. We have modified the enthalpy formulation in such a way that the enthalpy gradient term is not needed, and as a result of this modification, the computation stability and the computing time were improved.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1999년도 춘계학술대회논문집
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• pp.225-228
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• 1999

In a plastically deformed body the formation of a shear band is widely observed in the engineering materials during rapidly forming process for a thermally rate-sensitive material. The localized shear bond stems from evolution of a narrow region in which intensive plastic flow occurs. The shear band often plays as a precursor of the ductile fracture during a forming process. The objectives of this study are to investigate the localization behaivor by using numerical method thus predict the failure. In this work the implicit finite difference scheme is preformed due to the ease of covergence and the numerical stability. This study is based on an analysised material with hardening as well as thermally softening behavior which includes isotropy strain hardening. Furthermore this paper suggests that an anticipated and suggested a kinematic hardening constitutive equation be requried to predicte a more accurate strain level wherein a shear band occurs.

• 대한기계학회논문집
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• 제19권8호
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• pp.1950-1963
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• 1995

A modification of the approximate-factorization method is made to accelerate the convergency rate and to take sufficiently large Courant number without loss of accuracy. And a stable implicit finite-difference scheme for solving the incompressible Navier-Stokes equations employed above modified method is developed. In the present implicit scheme, the volume fluxes with contravariant velocity components and the pressure formulation in curvilinear coordinates is adopted. In order to satisfy the continuity condition completely and to remove spurious errors for the pressure, the Navier-Stokes equations are solved by a modified SMAC scheme using a staggered gird. The upstream-difference scheme such as the QUICK scheme is also employed to the right hand side. The implicit scheme is unconditionally stable and satisfies a diagonally dominant condition for scalar diagonal linear systems of implicit operator on the left hand side. Numerical results for some test calculations of the two-dimensional flow in a square cavity and over a backward-facing step are obtained using both usual approximate-factorization method and the modified one, and compared with each other. It is shown that the present scheme allows a sufficiently large Courant number of O(10$^{2}$) and reduces the computing time.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2000년도 봄 학술발표회 논문집
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• pp.631-638
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• 2000

Pioneering work by Terzaghi imparted scientific and mathematical bases to many aspects of this subject and many people use this theory to measure the consolidation settlement until now. In this paper, Finite Difference Methods for consolidation are considered. First, it is shown the stability criterion of Explicit scheme and the Crank-Nicolson scheme, although unconditionally stable in the mathematical sense, produces physically unrealistic solutions when the time step is large. it is also shown that The Fully Implicit scheme shows more satisfactory behavior, but is less accurate for small time steps. and then we need to decide what scheme is more proper to consolidation. The purpose of this paper is to suggest the pertinent scheme to consolidation.

• 소성∙가공
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• 제9권4호
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• pp.395-403
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• 2000

Formation of Shear Band under the adiabatic condition is widely observed In the engineering materials during rapidly forming process lot a thermally rate-dependent material. The shear band stems from evolution of a narrow region in which an intensive plastic flow occurs. The shear band often plays a role of a precursor of the ductile fracture during a forming process. The objective of this study is to investigate the localization behavior using numerical method. In this work, the implicit finite difference scheme is employed due to the ease of convergence and the numerical stability It is noted that physical and mechanical properties of materials determine how the shear band is formed and then localized. Material properties can be characterized with inertia number dissipation number and diffusion number. It is observed that the dimensionless numbers effect on localization. Using a parametric study, comparison was made between CRS-1018 steel with WHA (tungsten heavy alloy). The deformation behavior of material in this study include an isotropic hardening as well as thermal softening. Moreover, this study suggests that a kinematic hardening constitutive relation be required to predict a more accurate strain level at a shear band.

• Steel and Composite Structures
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• 제49권5호
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• pp.587-602
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• 2023

This article presents the numerical modelling of transient heat transfer in highly heterogeneous composite materials where the thermal conductivity, specific heat and density are assumed to be directional-dependent. This article uses a coupled finite element-finite difference scheme to perform the transient heat transfer analysis of unidirectional (1D) and multidirectional (2D/3D) functionally graded composite panels. Here, 1D/2D/3D functionally graded structures are subjected to nonuniform heat source and inhomogeneous boundary conditions. Here, the multidirectional functionally graded materials are modelled by varying material properties in individual or in-combination of spatial directions. Here, fully spatial-dependent material properties are evaluated using Voigt's micromechanics scheme via multivariable power-law functions. The weak form is obtained through the Galerkin method and solved further via the element-space and time-step discretisation through the 2D-isoparametric finite element and the implicit backward finite difference schemes, respectively. The present model is verified by comparing it with the previously reported results and the commercially available finite element tool. The numerous illustrations confirm the significance of boundary conditions and material heterogeneity on the transient temperature responses of 1D/2D/3D functionally graded panels.

• 한국수자원학회논문집
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• 제45권2호
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• pp.179-189
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• 2012

오염물질의 이동 현상을 모의하기 위하여, 감쇠항이 있는 3차원 이송-확산 방정식의 수치모형이 개발되었다. 개발된 모형은 유한차분 모형으로서 시간단계의 가중치 ${\alpha}$를 포함하는 음해법(implicit finite difference method)과, 반복법인 Gauss-Seidel SOR(successive over relaxation)이 사용되었다. 모형은 보다 단순화된 가정 하에서 존재하는 두 가지의 해석적인 해와 비교되었다. 그 결과 Peclet number가 5~20 이하에서는 수치 분산의 영향이 크지 않았고 작은 오차범위 내에서 해석적인 해와 동일하였다. 또한 가중치 ${\alpha}$의 변화에 대한 모형의 거동은 Crank-Nicolson 모형(${\alpha}$=0.5)이 fully-implicit 모형(${\alpha}$=1)보다 해석적인 해에 접근함을 보여주었다. 모형의 검증과 실효성 제고를 위하여, mass balance를 검토하였다. 즉, 이송, 확산 및 감쇠항 각각에 대한 질량 이동을 산출하였으며, 그 결과 질량 이동의 계산 오차는 약 3% 이내였다. 본 모형은 감쇠 과정이 수반되는 3차원 이송-확산의 농도분포와 질량이동을 산출할 수 있으며 다양한 경계조건을 설정함으로서 현장조건을 반영할 수 있다. 그러나본 모형은 고정격자를 기반으로하는 유한차분 모형이므로 Peclet number가 비교적 작게 나타날 수 있는 토양 및 지하수계의 오염물질 이동 등의 문제에서 유용하게 적용될 수 있을 것으로 사료된다.

• 정보저장시스템학회논문집
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• 제5권1호
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• pp.19-35
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• 2009

The present work is an experimental and analytical study on a flexible disk rotating close to a rigid rotating disk in open air. In the analytical study, the air flow in the gap between the flexible disk and the rigid disk is modeled using Navier-Stokes and continuity equations while the flexible disk is modeled using the linear plate theory. The flow equations are discretized using the cell centered finite volume method (FVM) and solved numerically with semi-implicit pressure-linked equations (SIMPLE algorithm). The spatial terms in the disk equation are discretized using the finite difference method (FDM) and the time integration is performed using fourth-order Runge-Kutta method. An experimental test-rig is designed to investigate the dynamics of the flexible disk when rotating close to a co-rotating, a counter-rotating and a fixed rigid disk, which works as a stabilizer. The effects of rotational speed, initial gap height and inlet-hole radius on the flexible disk displacement and its vibration amplitude are investigated experimentally for the different types of stabilizer. Finally, the analytical and experimental results are compared.