• 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.

• 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.

• Research in Mathematical Education
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• v.8 no.3
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• pp.175-182
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• 2004

The design of learning environments which encourage students to work in a creative manner on mathematical problems is a creative process in itself. The concept of the Saturday University program is described in which pre-service teachers are guided at teaching students in extra-curriculum activities on interdisciplinary topics. In the process of the didactical reconstruction of mathematical problems, the pre-service teachers go through the stages of a revolving door model y.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.97-113
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• 2004

In this paper we shall study moving boundary problems, and we introduce an approach for solving a wide range of them by using calculus of variations and optimization. First, we transform the problem equivalently into an optimal control problem by defining an objective function and artificial control functions. By using measure theory, the new problem is modified into one consisting of the minimization of a linear functional over a set of Radon measures; then we obtain an optimal measure which is then approximated by a finite combination of atomic measures and the problem converted to an infinite-dimensional linear programming. We approximate the infinite linear programming to a finite-dimensional linear programming. Then by using the solution of the latter problem we obtain an approximate solution for moving boundary function on specific time. Furthermore, we show the path of moving boundary from initial state to final state.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.10 no.1
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• pp.12-21
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• 1981

The Enthalpy Model was verified in order to analyze two- dimensional phase change problems. By using the Enthalpy Model, interface locations, frozen fraction rates, heat flux distribution rut cooled surfaces, and surface-integrated heat flux were purely numerically calculated in rectangular thermal storage units, whose initial condition was saturated liquid and phase change material was cooled on its boundaries by convective heat transfer. The calculations were performed for various Stefan numbers and Biot numbers. The effect on those dimensionless numbers were explained.

• Proceedings of the SAREK Conference
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• 2006.06a
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• pp.116-121
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• 2006

Numerical simulations for dendritic growth of crystals are conducted in this study by the level set method. The effect of order of difference is tested for reinitialization error in simple problems and authors founded in case of 1st order of difference that very fine grids have to be used to minimize the error and higher order of difference is desirable to minimize the reinitialization error The 2nd and 4th order Runge-Kutta scheme in time and 3rd and 5th order of WENO schemes with Godunov scheme are applied for space discretization. Numerical results are compared with the analytical theory, phase-field method and other researcher's level set method.

• Journal of Adhesion and Interface
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• v.7 no.4
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• pp.28-31
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• 2006

Due to the miniaturization of MEMS and microelectronics the joining techniques also have to be adjusted. The dosing technology with viscous adhesives does not permit reproducible adhesive volumes, which are clearly under a nano-liter. A nano-liter means however a diameter of bonding area within the range of several 100 micrometers. Additional, viscous adhesives need a certain time, until they are cross linked or cured. The problem especially in the MEMS is the initial strength, since it gives the time, which is needed for joining an individual adhesive joint. The time up to the initial strength is with viscous, also with fast curing systems, within the range of seconds until minutes. Until the reach of the initial strength, the micro part must be fixed/held. Without sufficient adjustment/clamping it can come to a shift of the micro parts. Also existing micro adhesive bonding processes are not batch able, i.e. the individual adhesive joints of a micro system must be processed successively. In the context of the WCARP III 2006 now an innovative method is to be presented, how it is possible to solve the existing problems with micro bonding. i.e. a method is presented, which is batch able, possess a minimum joining geometry with some micrometers and is so fast that no problems with the initial strength arise. It is a method, which could revolutionize the sticking technology in the micro system engineering.

• Geomechanics and Engineering
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• v.5 no.6
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• pp.575-594
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• 2013

Organic soils exhibit problematic properties such as high compressibility and low shear strength; these properties may cause differential settlement or failure in structures built on such soils. Organic soil removal or stabilization are the most important methods to overcome geotechnical problems related to peat soils' engineering characteristics. This paper presents soil mechanical intervention for stabilization of peat with sand columns and focuses on a comparison between the mechanical characteristics of undisturbed peat and peat stabilized with 20%, 30% and 40% of sand on the laboratory scale. Cylindrical columns were extruded in different diameters through a nearly undisturbed peat sample in the laboratory and filled with sand. By adding sand columns to peat, higher permeability, higher shear strength and a faster consolidation was achieved. The sample with 70% peat and 30% sand displayed the most reliable compressibility properties. This can be attributed to proper drainage provided by sand columns for peat in this specific percentage. It was observed that the granular texture of sand also increased the friction angle of peat. The addition of 30% sand led to the highest shear strength among all mixtures considered. The peat samples with 40% sand were sampled with two and three sand columns and tested in direct shear and consolidation tests to evaluate the influence of the number and geometry of sand columns. Samples with three sand columns showed higher compressibility and shear strength. Following the results of this laboratory study it appears that the introduction of sand columns could be suitable for geotechnical peat stabilization in the field scale.