• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.281-294
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• 2006

Many partial differential equations defined on a rectangular domain can be solved numerically by using a domain decomposition method. The most commonly used decompositions are the domain being decomposed in stripwise and rectangular way. Theories for non-overlapping domain decomposition(in which two adjacent subdomains share an interface) were often focused on the stripwise decomposition and claimed that extensions could be made to the rectangular decomposition without further discussions. In this paper we focus on the comparisons of the two ways of decompositions. We consider the unconditionally stable scheme, the MIP algorithm, for solving parabolic partial differential equations. The SOR iterative method is used in the MIP algorithm. Even though the theories are the same but the performances are different. We found out that the stripwise decomposition has better performance.

• Journal of Korea Foundry Society
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• v.14 no.5
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• pp.412-418
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• 1994

Efficient algorithm for the solidification simulation by FDM is described from the practical point of views. If a proper time step ${\Delta}t$ is selected, the calculation is accelerated by implicit algorithm with the temperature recovery method of latent heat method. The implicit routine in the calculation is processed by SOR method(relaxation factor＝1.5, truncation error＝$10^{-4}$). The calculation is more accelerated by linear-interpolated explicite algorithm with a time step larger than the minimum value of the time step. This explicit method, which is applicable to the practical casting simulation problems, produces almost same results with about 40% faster calculation speed compared with the conventional explicit method.

• Electrical & Electronic Materials
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• v.10 no.10
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• pp.1000-1004
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• 1997

In this paper the current-voltage characteristics of a submicron GaAs MESFET is simulated by using the self-consistent ensemble Monte Carlo method. The numerical algorithm employed in solving the two-dimensional Poisson equation is the successive over-relaxation(SOR) method. The total number of employed superparticles is about 1000 and the field adjusting time is 10fs. To obtain the steady-state results the simulation is performed for 10ps at each bias condition. The simulation results show the average electron velocity is modified by the gate voltage.

• Smart Structures and Systems
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• v.24 no.6
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• pp.683-692
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• 2019

Traditional damage detection methods for nonlinear structures are often based on simplified models, such as the mass-spring-damper and shear-building models, which are insufficient for predicting the vibration responses of a real structure. Conventional global nonlinear finite element model updating methods are computationally intensive and time consuming. Thus, they cannot be applied to practical structures. A decentralized approach for identifying the nonlinear material parameters is proposed in this study. With this technique, a structure is divided into several small zones on the basis of its structural configuration. The unknown material parameters and measured vibration responses are then divided into several subsets accordingly. The structural parameters of each subset are then updated using the vibration responses of the subset with the Newton-successive-over-relaxation (SOR) method. A reinforced concrete and steel frame structure subjected to earthquake loading is used to verify the effectiveness and accuracy of the proposed method. The parameters in the material constitutive model, such as compressive strength, initial tangent stiffness and yielding stress, are identified accurately and efficiently compared with the global nonlinear model updating approach.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.41 no.9
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• pp.571-577
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• 2017

In this numerical study, the separation efficiency of three-phase separator in an oil-sand plant was studied with various inlet head configurations. The free water knockout (FWKO) vessel was designed with a flow rate of $15.89m^3/day$ (100 bbl/day) and the SOR(stream-to-oil ratio)=3.5 was derived using Stokes' law. For modularization, optimization of the design of the inlet head configuration was performed with parallel-connected dual FWKO vessels. The feed condition of bitumen emulsion was API=17, $T_{in}=150^{\circ}C$ and $P_{in}=50bar$. A mean residence time was determined the time when 95% of the oil and water in FWKO vessel was separated. The combination between the volume of fluid (VOF) and the discrete phase model (DPM) was used to simulate the phase separation phenomenon in a multi-phase separator. Furthermore, in order to calculate multi-phase flow the pseudo-transient method was adopted.

• Journal of information and communication convergence engineering
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• v.10 no.1
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• pp.66-70
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• 2012

Conformal mapping has been a familiar tool of science and engineering for generations. Determination of a conformal map from the unit disk onto the Jordan region is reduced to solving the Theodorsen equation, which is an integral equation for boundary correspondence functions. There are many methods for solving the Theodorsen equation. It is the goal of numerical conformal mapping to find methods that are at once fast, accurate, and reliable. In this paper, we analyze Niethammer’s solution based on successive over-relaxation (SOR) iteration and Wegmann’s solution based on Newton iteration, and compare them to determine which one is more effective. Through several numerical experiments with these two methods, we can see that Niethammer’s method is more effective than Wegmann’s when the degree of the problem is low and Wegmann’s method is more effective than Niethammer’s when the degree of the problem is high.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.4 no.2
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• pp.35-43
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• 1984

The purpose of this paper is to develop a mathematical model which can be used to compute the position of the free surface due to water level fluctuations in the canal and the transient pressure distributions along the canal lining. The diagnostic equation has been solved by the point successive over-relaxation method, and the linearized prognostic equation has been solved by the implicit Lax-Wendroff scheme. Four different cases in the simulation conditions are presented for both permeable and impermeable canal lining to predict the transient seepage surface development.

• Fire Science and Engineering
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• v.6 no.1
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• pp.17-22
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• 1992

We have derived the general transfer equation for governing the continuity, energy transfer, mass and momentum transfer, and turbulent energy dissipation rate within the fire compartment which has the 800t fire source at the center of the floor. The governing transfer equations have been descretized using the finite volume approach and numerically experimented under the SIMPLE algorithm. In order for the SIMPLE algorithm approach to be physically reliable, the test results are compared with those of Morita's SOR Method using Conjugate Residual Method and found to be close to physical values though the computational convergence time still remains to be upgraded. The treatment of source terms in the system of finite difference equations has been critical in order to converge the governing equations within the appropriate time steps. The criteria of convergence allowance for the whole domain have been checked and the sudden change of the non-linear effects from the source term have been avoided. The criteria has been allowed to be for 5$\times$10$^{-5}$ .

• Tribology and Lubricants
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• v.12 no.2
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• pp.65-73
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• 1996

Rapid increase of Refrigeration and Air conditioning system in modem industries brings attention to the urgency of core technology development in the area. This paper presents theoretical investigation of the lubrication characteristics of rotary compressor for refrigeration and air conditioning. In order to analyze the lubrication characteristics of the main & sub bearing of rotary compressor, the bearing force and locus of shaft center are analyzed by the dynamic analysis of rotary compressor and numerical analysis of Reynolds equation as the operating condition is changed in various ways. In this paper, we used the Runge-Kutta method for the dynamic analysis of rotary compressor and the SOR (Successive OverRelaxation) method for the numerical analysis of Reynolds equation. The result shows that the operating condition of sub bearing is severer than that of main bearing, and eccentricity ratio grows as the bearing force increases. It is believed that the result can be applied to the design of alternative refrigerant rotary compressor.

• 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.