• 한국전산유체공학회:학술대회논문집
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• 1999.11a
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• pp.59-64
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• 1999

The Equations of Chemical kinetics ate very stiff, which forces the use of an implicit scheme. The problem of implicit scheme, however, is that the jacobian must be solved at each time step. In this paper, we examined the approximate chemical jacobian methods such as Gauss-Seidel, Jacobi partial jacobian and diagonalized jacobian that can be stable without full jacobian, We show that Gauss-Seidel jacobian method is stable and accurate as well as full jacobian and that this is more efficient in supersonic combustion problem about $20\%$ than the full jacobian method with same accuracy,

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.135-142
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• 2000

We consider a multigrid algorithm for higher order finite difference scheme for the Poisson problem on rectangular domain. Several smoothers including Jacobi, Red-black Gauss-Seidel are tested and compared. Since higher order scheme gives much more accurate result then 5-point scheme, one may use small number of levels with higher order scheme and thus the overall cost is reduced quite a lot. The numerical experiment compares the two cases.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.25 no.5
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• pp.601-606
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• 2014

The IPO(Iterative Physical Optics) method repeatedly applies the well-known PO(Physical Optics) approximation to calculate the scattered field by a large object. Thus, the IPO method can consider the multiple scattering in the object, which is ignored for the PO approximation. This kind of iteration can improve the final accuracy of the induced current on the scatterer, which can result in the enhancement of the accuracy of the RCS(Radar Cross Section) of the scatterer. Since the IPO method can not exactly but approximately solve the required integral equation, however, the convergence of the IPO solution can not be guaranteed. Hence, we apply the famous techniques used in the inversion of a matrix to the IPO method, which include Jacobi, Gauss-Seidel, SOR(Successive Over Relaxation) and Richardson methods. The proposed IPO methods can efficiently calculate the RCS of a large scatterer, and are numerically verified.

• Nuclear Engineering and Technology
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• v.54 no.2
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• pp.532-545
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• 2022

In-depth convergence analyses for neutronics/thermal-hydraulics (T/H) coupled calculations are performed to investigate the performance of nonlinear methods based on the Fixed-Point Iteration (FPI). A simplified neutronics-T/H coupled system consisting of a single fuel pin is derived to provide a testbed. The xenon equilibrium model is considered to investigate its impact during the nonlinear iteration. A problem set is organized to have a thousand different fuel temperature coefficients (FTC) and moderator temperature coefficients (MTC). The problem set is solved by the Jacobi and Gauss-Seidel (G-S) type FPI. The relaxation scheme and the Anderson acceleration are applied to improve the convergence rate of FPI. The performances of solution schemes are evaluated by comparing the number of iterations and the error reduction behavior. From those numerical investigations, it is demonstrated that the number of FPIs is increased as the feedback is stronger regardless of its sign. In addition, the Jacobi type FPIs generally shows a slower convergence rate than the G-S type FPI. It also turns out that the xenon equilibrium model can cause numerical instability for certain conditions. Lastly, it is figured out that the Anderson acceleration can effectively improve the convergence behaviors of FPI, compared to the conventional relaxation scheme.

• International Journal of Aeronautical and Space Sciences
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• v.8 no.2
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• pp.44-53
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• 2007

A three-dimensional viscous flow solver has been developed for the prediction of the aerodynamic performance of hovering helicopter rotor blades using unstructured hybrid meshes. The flow solver utilized a vertex-centered finite-volume scheme that is based on the Roe's flux-difference splitting with an implicit Jacobi/Gauss-Seidel time integration. The eddy viscosity are estimated by the Spalart- Allmaras one-equation turbulence model. Calculations were performed at three operating conditions with varying tip Mach number and collective pitch setting for the Caradonna-Tung rotor in hover. Additional computations are made for the UH-60A rotor in hover. Reasonable agreements were obtained between the present results and the experiment in both blade loading and overall rotor performance. It was demonstrated that the present vertex-centered flow solver is an efficient and accurate tool for the assessment of rotor performance in hover.

• Structural Engineering and Mechanics
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• v.48 no.2
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• pp.241-255
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• 2013

The receding contact problem for two elastic layers whose elastic constants and heights are different supported by two elastic quarter planes is considered. The lower layer is supported by two elastic quarter planes and the upper elastic layer is subjected to symmetrical distributed load whose heights are 2a on its top surface. It is assumed that the contact between all surfaces is frictionless and the effect of gravity force is neglected. The problem is formulated and solved by using Theory of Elasticity and Integral Transform Technique. The problem is reduced to a system of singular integral equations in which contact pressures are the unknown functions by using integral transform technique and boundary conditions of the problem. Stresses and displacements are expressed depending on the contact pressures using Fourier and Mellin formula technique. The singular integral equation is solved numerically by using Gauss-Jacobi integration formulation. Numerical results are obtained for various dimensionless quantities for the contact pressures and the contact areas are presented in graphics and tables.

• 한국전산유체공학회:학술대회논문집
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• 2008.03b
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• pp.25-28
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• 2008

An aerodynamic calculation in hover of KUH main rotor blade is performed using a three-dimensional unstructured hybrid mesh viscous flow solver. The flow solver utilizes a vertex-centered finite-volume scheme that is based on the Roe's flux-difference splitting with an implicit Jacobi/Gauss-Seidel time integration. The eddy viscosity are estimated by the Spalart-Allmaras one-equation turbulence model. A solution-adaptive mesh refinement technique is used for efficient capturing of the tip vortex. Calculations are performed at several operating conditions with varying collective pitch setting for KUH main rotor blade in hover. Good agreements are obtained between the present and other results using HOST and CAMRAD II in overall rotor performance. It is demonstrated that the present vertex-centered flow solver is an efficient and accurate tool for the assessment of rotor performance in hover.

• Structural Engineering and Mechanics
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• v.64 no.4
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• pp.505-513
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• 2017

In this paper, a receding contact problem for an elastic layer resting on a half plane is considered. The layer is pressed by two rectangular stamps placed symmetrically. It is assumed that the contact surfaces are frictionless and only compressive traction can be transmitted through the contact surfaces. In addition the effect of body forces is neglected. Firstly, the problem is solved analytically based on theory of elasticity. In this solution, the problem is reduced into a system of singular integral equations in which half contact length and contact pressures are unknowns using boundary conditions and integral transform techniques. This system is solved numerically using Gauss-Jacobi integral formulation. Secondly, two dimensional finite element analysis of the problem is carried out using ANSYS. The dimensionless quantities for the contact length and the contact pressures are calculated under various stamp size, stamp position and material properties using both solutions. The analytic results are verified by comparison with finite element results.

• Proceedings of the ESK Conference
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• 1997.10a
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• pp.463-467
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• 1997

인간에게 운동감을 적절히 제시해주기 위하여는 Newton에 의한 운동의 세가지 법칙뿐만 아니라 EInstein의 상대성이론이 첨가되어야 한다. 즉, Newton운동의 제1법칙에 의하여 피실험자가 외력을 받지 않으면 등속운동 또는 정지상태를 계속 유지하게 되어 자신이 등속좌표계에 고정되어있기 때문에 시각적 인 정보가 없으면 어떠한 운동감도 못 느낀다. 이때 피실험자에게 정지해있는 기준좌표계에 대하여 등속 으로 움직이는 것을 인식시켜주기 위하여 피실험자에 대한 기준좌표계의 상대속도를 시각정보로 제공해 주어야 한다. 또한 Newton운동의 제2법칙에 의하여 똑같은 힘이 외력으로 작용하더라도 피실험자의 질량과 가속도는 서로 반비례하므로 화면이동속도변화를 피실험자의 질량에 반비례하도록 제시해 주어야 한다(김 정흠, 1982). 본 연구에서는 이러한 개념에 근거하여, 체중이 다른 여섯 피실험자들로 구성된 시스템에 대해서 각 피실험자에게 서로 다른 변위를 주고자할 때, 여섯가지 외력에 요구되는 작용시간을 Jacobi Iteration 방법과 Gauss-Seidel Iteration 방법으로 구하는 알고리즘을 제시하였다(D.V. Griffiths and I.M. Smith, 1991).

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.101-124
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• 2002

The convergence rate of a numerical procedure barred on Schwarz Alternating Method (SAM) for solving elliptic boundary value problems (BVP's) depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It hee been observed that the Robin condition(mixed interface condition), controlled by a parameter, can optimize SAM's convergence rate. Since the convergence rate is very sensitive to the parameter, Tang[17] suggested another interface condition called over-determined interface condition. Based on the over-determined interface condition, we formulate the two-layer multi-parameterized SAM. For the SAM and the one-dimensional elliptic model BVP's, we determine analytically the optimal values of the parameters. For the two-dimensional elliptic BVP's , we also formulate the two-layer multi-parameterized SAM and suggest a choice of multi-parameter to produce good convergence rate .