• Proceedings of the KSME Conference
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• 2001.06e
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• pp.588-594
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• 2001

본 연구를 통해 초음속 전투기 날개의 공력-구조를 동시에 고려한 다학제간 설계를 수행하였다. 공력해석을 위해 사용된 3 차원 Euler Code는 수렴 속도를 개선하기 위해 Multigrid를 적용하였으며, 3차의 transfinite interpolation을 사용하여 O-H type의 공력해석 격자계를 생성하였다. 구조 분야는 절점당 54개의 자유도를 가지는 9 절점 쉘 혼합 유한요소(9-node shell mixed finite element)를 사용하여 해석을 수행하였다. 설계변수는 공력쪽으로 날개의 평면형상에 관련된 변수 3개, 구조쪽은 날개 윗면과 아래면의 표피두께에 관련된 4개의 설계변수 사용하였으며, D-optimality 조건을 만족시키는 실험점들에 대해 공력해석과 구조해석이 연동된 정적 공탄성 해석을 수행한 후, 반응면 기법을 이용하여 목적함수와 제약조건에 대한 반응면을 구성하였다. 단일점 설계를 수행한 후 이를 바탕으로 3개의 설계점을 동시에 고려한 다점 설계를 수행하였으며, 공력만을 고려한 설계 결과와 공력-구조를 동시에 고려한 다학제간 설계결과의 비교를 통해 다학제간 설계의 타당성과 우수성을 입증하였다.

• Journal of the Korean Society of Visualization
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• v.16 no.2
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• pp.23-30
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• 2018

The present study compares flow fields reconstructed by data assimilation method with different combinations of parameters. As a data assimilation method, Vortex-in-Cell-sharp (VIC#), which supplements additional constraints and multigrid approximation to Vortex-in-Cell-plus (VIC+), is used to reconstruct flow fields from scattered particle tracks. Two parameters, standard deviation of Gaussian radial basis function (RBF) and grid spacing, are mainly tested using artificial data sets which contain few particle tracks. Consequent flow fields are analyzed in terms of flow structure sizes. It is demonstrated that sizes of the flow structures are proportional to an actual scale of the standard deviation of RBF. It implies that a combination of larger grid spacing and smaller standard deviation which preserves the actual standard deviation is able to save computational resources in case of a low track density. In addition, a simple comparison using an experimental data filled with dense particle tracks is conducted.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.8
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• pp.8-17
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• 2005

It is well known that preconditioning methods are efficient for convergence acceleration in the compressible low Mach number flows. In this study, the original Euler equations and three differently nondimensionalized preconditioning methods are implemented in two dimensional inviscid bump flows using the 3rd order MUSCL and DADI schemes as numerical flux discretization and time integration, respectively. The multigrid and local time stepping methods are also used to accelerate the convergence. The test case indicates that a properly modified local preconditioning technique involving concepts of a global preconditioning allows Mach number independent convergence. Besides, an asymptotic analysis for properties of preconditioning methods is added.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.3
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• pp.197-207
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• 2013

The Cahn-Hilliard equation was proposed as a phenomenological model for describing the process of phase separation of a binary alloy. The equation has been applied to many physical applications such as amorphological instability caused by elastic non-equilibrium, image inpainting, two- and three-phase fluid flow, phase separation, flow visualization and the formation of the quantum dots. To solve the Cahn-Hillard equation, many numerical methods have been proposed such as the explicit Euler's, the implicit Euler's, the Crank-Nicolson, the semi-implicit Euler's, the linearly stabilized splitting and the non-linearly stabilized splitting schemes. In this paper, we investigate each scheme in finite-difference schemes by comparing their performances, especially stability and efficiency. Except the explicit Euler's method, we use the fast solver which is called a multigrid method. Our numerical investigation shows that the linearly stabilized stabilized splitting scheme is not unconditionally gradient stable in time unlike the known result. And the Crank-Nicolson scheme is accurate but unstable in time, whereas the non-linearly stabilized splitting scheme has advantage over other schemes on the time step restriction.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.2
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• pp.181-186
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• 2022

Poisson-Boltzmann equation (PBE) is used to model problems arising from various disciplinary including bio-pysics and colloid chemistry. Therefore, to predict a numerical solution of PBE is an important issue. The authors proposed deep learning based methods to solve PBE while the computational time to generate finite element method (FEM) solutions were bottlenecks of the algorithms. In this work, we shorten the generation time of FEM solutions in two directions. First, we experimentally find certain penalty parameter in a bilinear form. Second, we applied algebraic multigrids methods to the algebraic system so that condition number is bounded regardless of the meshsize. In conclusion, we have reduced computation times to solve algebraic systems for PBE. We expect that algebraic multigrids methods can be further employed in various disciplinary to generate deep learning samples.