• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2010년 춘계학술대회논문집
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• pp.534-541
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• 2010

A high-order accurate Euler flow solver based on a discontinuous Galerkin method has been developed for the numerical simulation of unsteady flows on unstructured meshes. A multi-level solution-adaptive mesh refinement/coarsening technique was adopted to enhance the resolution of numerical solutions efficiently by increasing mesh density in the high-gradient region. An acoustic wave scattering problem was investigated to assess the accuracy of the present discontinuous Galerkin solver, and a supersonic flow in a wind tunnel with a forward facing step was simulated by using the adaptive mesh refinement technique. It was shown that the present discontinuous Galerkin flow solver can capture unsteady flows including the propagation and scattering of the acoustic waves as well as the strong shock waves.

• Advances in nano research
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• 제7권5호
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• pp.311-324
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• 2019

The present study aims to evaluate the nonlinear and post-buckling behaviors of orthotropic graphene sheets exposed to end-shortening strain by implementing a semi-Galerkin technique, as a new approach. The nano-sheets are regarded to be on elastic foundations and different out-of-plane boundary conditions are considered for graphene sheets. In addition, nonlocal elasticity theory is employed to achieve the post-buckling behavior related to the nano-sheets. In the present study, first, out-of-plane deflection function is considered as the only displacement field in the proposed technique, which is hypothesized by an appropriate deflected form. Then, the exact nonlocal stress function is calculated through a complete solution of the von-Karman compatibility equation. In the next step, Galerkin's method is used to solve the unknown parameters considered in the proposed technique. In addition, three different scenarios, which are significantly different with respect to concept, are used to satisfy the natural in-plane boundary conditions and completely attain the stress function. Finally, the post-buckling behavior of thin graphene sheets are evaluated for all three different scenarios, and the impacts of boundary conditions, polymer substrate, and nonlocal parameter are examined in each scenario.

• 한국해안해양공학회지
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• 제6권2호
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• pp.174-185
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• 1994

본 논문에서는 수평유속의 연직방향 변화 결정에 유한요소기법(FEM)을 이용하고 수평방향으로는 유한차분기법을 사용하는 복합형 Galerkin 연직함수 전개모델에 새로이 유사변환기법을 추가한 3차원 해수유동모델의 개발에 대하여 기술하였다. 기본방정식의 연직방향으로 선형보간함수를 기저함수로 사용하여 Galerkin 기법을 적용하여 구성되는 행열 방정식에 유사변환기법을 적용, 각 절점의 유속값을 해석적으로 구하였다. 유사변환기법을 적용하여 최종 얻어지는 모우드 shape 방정식은 비연계된 방정식으로 구성되므로 역행렬 계산이 필요없어 계산시간이 절약된다. 또한 수립된 모델은 고유벡터행렬로 구성되는 모우드 shape가 도입됨으로써 모우드 shape 몇개만 사용하여도 거의 수렴된 값을 얻을 수 있어 계산시간을 절약할 수 있다. 등수심하 유한영역과 무한영역에서의 수치실험을 통하여 개발된 모델의 적용 가능성을 검증하였다.

• 한국전자파학회논문지
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• 제23권4호
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• pp.541-550
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• 2012

본 논문에서는 3차원 공간의 전자파 수치 해석을 위한 모멘트법(method of moments)의 개선된 해석 기법을 선보인다. 전자파 산란 특성을 해석하기 위해 기본적으로 EFIE(Electric Field Integral Equation)와 RWG(Rao-Wilton-Glisson) 기저 함수를 이용하였으며, 계산 효율을 높이기 위해 기존의 갤러킨(Galerkin) 기법과 중심점 보간(interpolation)법을 혼용하여 해석 시간을 단축시켰다. 이때, 계산 정확도 유지를 위해 임피던스 행렬의 각 원소간 거리를 상대 거리 지수로 정의하여 보간법 적용이 가능한 먼 거리 원소를 구분하였다. 제안된 해석 기법의 성능 검증은 금속구의 Mie-series 해법을 이용한 이론적 RCS(Radar Cross Section)를 비교/분석하였다. 또한, 본 연구 결과를 삼면-/전방향- 전파반사기와 같은 산란체에 적용하여 레이더 후방 산란 특성을 분석하였다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 학술대회
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• pp.57-70
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• 2008

A high-order accurate Euler flow solver based on a discontinuous Galerkin finite-element method has been developed for the numerical simulations of blade-vortex interaction phenomena on unstructured meshes. A free vortex in freestream was investigated to assess the vortex-preserving property and the accuracy of the present flow solver. Blade-vortex interaction problems in subsonic and transonic freestreams were simulated by adopting a multi-level solution-adaptive dynamic mesh refinement/coarsening technique. The results were compared with those of other numerical and experimental methods. It was shown that the present discontinuous Galerkin flow solver can preserve the vortex structure for significantly longer vortex convection time and can accurately capture the complex unsteady blade-vortex interaction flows, including generation and propagation of acoustic waves.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년 추계학술대회논문집
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• pp.57-70
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• 2008

A high-order accurate Euler flow solver based on a discontinuous Galerkin finite-element method has been developed for the numerical simulations of blade-vortex interaction phenomena on unstructured meshes. A free vortex in freestream was investigated to assess the vortex-preserving property and the accuracy of the present flow solver. Blade-vortex interaction problems in subsonic and transonic freestreams were simulated by adopting a multi-level solution-adaptive dynamic mesh refinement/coarsening technique. The results were compared with those of other numerical and experimental methods. It was shown that the present discontinuous Galerkin flow solver can preserve the vortex structure for significantly longer vortex convection time and can accurately capture the complex unsteady blade-vortex interaction flows, including generation and propagation of acoustic waves.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 추계학술대회
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• pp.1274-1279
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• 2003

In this paper, a new meshfree technique which improves the numerical integration accuracy is introduced. This new method called the Petrov-Galerkin natural element(PG-NE) is based on the Voronoi diagram and the Delaunay triangulation which is based on the same concept used for conventional natural element method called the Bubnov-Galerkin natural element(BG-NE). But, unlike BG-NE method, the test shape function is differently chosen from the trial shape function. The proposed technique ensures that the numerical integration error is remarkably reduced.

• 충청수학회지
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• 제32권3호
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• pp.261-280
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• 2019

We apply a reduced-order method based on B-spline Galerkin finite elements formulation to Rosenau-RLW equation for the first time and explain their process in detail. The ensemble of snapshots is very large generally, and it is difficult to apply POD to the ensemble of snapshots directly. Hence, we try to pick up important snapshots among the whole data. In this paper, we represent three different reduced-order schemes. First, the classical POD technique is examined. Second, (equally sampled snapshots) are exploited for POD technique. Finally, afterward sampling snapshots by CVT, for those snapshots, POD technique is implemented again.

• 한국전산구조공학회논문집
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• 제18권2호
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• pp.103-111
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• 2005

본 논문에서는 수치적분 정도를 향상시킬 수 있는 새로운 무요소 기법을 제안한파 저자들에 의해 페트로프-갤러킨 자연요소법(PG-NEM)이라 명명된 이 새로운 기법은 보로노이 다이어그램과 델라우니 삼각화에 기반을 두고 있으며, 이는 BG-NEM이라 불리는 기존의 자연요소법과 개념적으로 동일하다. 하지만, 동일한 시험 형상함수와 시도 형상함수를 선택하는 BG-NEM과는 달리, PG-NEM에서는 지지영역이 적분을 위한 배경격자에 정확하게 일치하도록 시험 형상함수를 독립적으로 선택하는 페트로프-갤러킨 개념에 기반을 두고 있다. 따라서, 제안된 기법은 BG-NEM과 비교하여 수치적분 정도를 현저히 향상시킬 것으로 기대된다.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.317-329
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• 2006

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.