• 대한수학회논문집
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• 제18권4호
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• pp.767-779
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• 2003

We consider a model of population dynamics whose mortality function is unbounded. We approximate the solution of the model using a discontinuous Galerkin finite element for the age variable and a backward Euler for the time variable. We present several numerical examples. It is experimentally shown that the scheme converges at the rate of $h^{3/2}$ in the case of piecewise linear polynomial space.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 추계학술대회
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• pp.474-479
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• 2004

According to our previous study, it is confirmed that the Petrov-Galerkin natural element method (PGNEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin natural element method (BG-NEM). This paper is an extension of PG-NEM to two-dimensional nonlinear dynamic problem. For the analysis, a constant average acceleration method and a linearized total Lagrangian formulation is introduced with the PG-NEM. At every time step, the grid points are updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates the nonlinear dynamic problem.

• 한국통신학회논문지
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• 제24권10B호
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• pp.1885-1894
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• 1999

본 논문에서는 Crawford TEM cell들의 고조 모드 차단 주파수에 대한 해석 결과를 나타내었다. 1/2 모드 경계영역을 제시하고, 변수 분리에 기초한 Galerkin 법을 적용하여 해석하였다. 대칭형은 물론 비대칭형 TEM 셀에 대한 차단 주파수를 정확히 예측할 수 있었다. 기존 대칭형 TEM cell과 직접 제작된 비대칭형 TEM cell에 적용한 결과 측정치와 매우 일치하고 있음을 볼 수 있었다.

• 한국전산유체공학회지
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• 제12권3호
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• pp.29-40
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• 2007

An implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes. The method can achieve high-order spatial accuracy by using hierachical basis functions based on Legendre polynomials. Numerical tests were conducted to estimate the convergence order of numerical solutions to the Ringleb flow and the supersonic vortex flow for which analytic solutions are available. Also, the flows around a 2-D circular cylinder and an NACA0012 airfoil were numerically simulated. The numerical results showed that the implicit discontinuous Galerkin methods couples with a high-order representation of curved solid boundaries can be an efficient method to obtain very accurate numerical solutions on unstructured meshes.

• 한국전산유체공학회지
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• 제16권4호
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• pp.72-83
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• 2011

A high-order discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equations was developed on unstructured triangular meshes. For this purpose, the BR2 methd(the second Bassi and Rebay discretization) was adopted for space discretization and an implicit Euler backward method was used for time integration. Numerical tests were conducted to estimate the convergence order of the numerical solutions of the Poiseuille flow for which analytic solutions are available for comparison. Also, the flows around a flat plate, a 2-D circular cylinder, and an NACA0012 airfoil were numerically simulated. The numerical results showed that the present implicit discontinuous Galerkin method is an efficient method to obtain very accurate numerical solutions of the compressible Navier-Stokes equations on unstructured meshes.

• 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.

• 대한기계학회논문집B
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• 제29권6호
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• pp.703-710
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• 2005

A finite element discretization of the advection and redistancing equations of level set method has been studied. It has been shown that Galerkin spatial discretization combined with Crank-Nicolson temporal discretization of the advection equation of level set yields a good result and that consistent streamline upwind Petrov-Galerkin(CSUPG) discretization of the redistancing equation gives satisfactory solutions for two test problems while the solutions of streamline upwind Petrov-Galerkin(SUPG) discretization are dissipated by the numerical diffusion added for the stability of a hyperbolic system. Furthermore, it has been found that the solutions obtained by CSUPG method are comparable to those by second order ENO method.

• 대한기계학회논문집A
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• 제24권8호
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• pp.2091-2099
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• 2000

The object of the present study is to present an adaptive wavelet-Galerkin method for the analysis of thin-walled box beam. Due to good localization properties of wavelets, wavelet methods emerge as alternative efficient solution methods to finite element methods. Most structural applications of wavelets thus far are limited in fixed-scale, non-adaptive frameworks, but this is not an appropriate use of wavelets. On the other hand, the present work appears the first attempt of an adaptive wavelet-based Galerkin method in structural problems. To handle boundary conditions, a fictitous domain method with penalty terms is employed. The limitation of the fictitious domain method is also addressed.

• Steel and Composite Structures
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• 제24권5호
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• pp.523-536
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• 2017

A layerwise (LW) formulation based on the Galerkin method is presented to investigate the three-dimensional stress state in long sandwich plate which is subjected to tension force and pure bending moment. Based on the Galerkin method and the LW discretization approach, the equilibrium equations of elasticity for the long plate are written in the weak form and discretized through the thickness of the plate. The discretized equations are written in terms of displacement components of the numerical layers. The governing equations of the plate are solved analytically for the free edge boundary conditions. The distribution of stress state especially the 3D stress state in the vicinity of the edges of the sandwich plate which is subjected to tension and pure bending is studied. In order to increase the accuracy, the out of plane stresses are obtained by integrating the equilibrium equations of elasticity. The convergence and accuracy of the predictions are studied and various numerical results are presented for distribution of the in-plane and out of plane stresses in symmetric and un-symmetric sandwich plates.