• 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 Korea Foundry Society
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• v.13 no.4
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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.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.03b
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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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.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.03b
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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.

• Transactions of Materials Processing
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• v.9 no.4
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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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• v.49 no.5
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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.

• Journal of Korea Water Resources Association
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• v.45 no.2
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• pp.179-189
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• 2012

To simulate the transport of pollutant, a numeric model for the advection-diffusion equation with the decay term is developed. This is finite-difference model using the implicit method (with the weight factor ${\alpha}$) and Gauss-Seidel SOR(successive over-relaxation). This model is compared to the analytical solutions (of simpler dimensional or boundary conditions), and in the condition of Peclet number < 5~20, the result shows stable condition, and Crank-Nicolson method (${\alpha}$=0.5) shows the more accurate results than fully-implicit method (${\alpha}$=1). The mass of advection, diffusion and decay is calculated and the error of mass balance is less than 3%. This model can evaluate the 3-D concentrations of the advection-diffusion and decay problems, but this model uses only the finite-difference method with the fixd grid system, so it can be effectively used in the problems with small Peclet numbers like the pollutant transport in groundwater.

• Transactions of the Society of Information Storage Systems
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• v.5 no.1
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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.