• 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 2007년도 춘계 학술대회논문집
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• pp.30-40
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• 2007

The implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes, which can achieve higher-order accuracy by wing 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. And, the flows around a circle and a NACA0012 airfoil was also numerically simulated. Numerical results show that the implicit discontinuous Galerkin methods with higher-order representation of curved solid boundaries can be an efficient higher-order method to obtain very accurate numerical solutions on unstructured meshes.

• Coupled systems mechanics
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• 제10권1호
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• pp.79-102
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• 2021

In this paper we deal with instability problems of structures under nonconservative loading. It is shown that such class of problems should be analyzed in dynamics framework. Next to analytic solutions, provided for several simple problems, we show how to obtain the numerical solutions to more complex problems in efficient manner by using the finite element method. In particular, the numerical solution is obtained by using a modified Euler-Bernoulli beam finite element that includes the von Karman (virtual) strain in order to capture linearized instabilities (or Euler buckling). We next generalize the numerical solution to instability problems that include shear deformation by using the Timoshenko beam finite element. The proposed numerical beam models are validated against the corresponding analytic solutions.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.215-222
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• 2000

A multigrid algorithm is developed for solving the one- dimensional initial boundary value problem. The numerical solutions of linear and nonlinear Burgers; equation for various initial conditions are studied. The stability conditions are derived by Von -Neumann analysis . Numerical results are presented.

• 대한수학회보
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• 제45권1호
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• pp.191-205
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• 2008

In this paper, we construct the analytic solutions and numerical solutions for a two-dimensional Riemann problem for Burgers' equation. In order to construct the analytic solution, we use the characteristic analysis with the shock and rarefaction base points. We apply the composite scheme suggested by Liska and Wendroff to compute numerical solutions. The result is coincident with our analytic solution. This demonstrates that the composite scheme works pretty well for Burgers' equation despite of its simplicity.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권1호
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• pp.45-51
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• 2017

In this paper, we propose an accelerating scheme of convergence of numerical solutions of fuzzy non-linear equations. Numerical experiments show that the new method has significant acceleration of convergence of solutions of fuzzy non-linear equation. Three-dimensional graphical representation of fuzzy solutions is also provided as a reference of visual convergence of the solution sequence.

• 대한수학회논문집
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• 제13권4호
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• pp.875-888
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• 1998

The use of the zeros of Chebyshev polynomial of the first kind $T_{4n＋4(x}$ ) and second kind $U_{2n＋1}$ (x) for Gauss-Chebyshev quad-rature and collocation of singular integral equations of Cauchy type yields computationally accurate solutions over other combinations of $T_{n}$ /(x) and $U_{m}$(x) as in [8]. We show that the coefficient matrix of the overdetermined system has the generalized inverse. We estimate the residual error using the norm of the generalized inverse.e.

• 대한기계학회논문집B
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• 제24권9호
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• pp.1227-1238
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• 2000

This study examines the effects of the discretization schemes on numerical solutions of viscoelastic fluid flows. For this purpose, a temporally evolving mixing layer, a two-dimensional vortex pair interacting with a wall, and a turbulent channel flow are selected as the test cases. We adopt a fourth-order compact scheme (COM4) for polymeric stress derivatives in the momentum equations. For convective derivatives in the constitutive equations, the first-order upwind difference scheme (UD) and artificial diffusion scheme (AD), which are commonly used in the literature, show most stable and smooth solutions even for highly extensional flows. However, the stress fields are smeared too much and the flow fields are quite different from those obtained by higher-order upwind difference schemes for the same flow parameters. Among higher-order upwind difference schemes, a third-order compact upwind difference scheme (CUD3) shows most stable and accurate solutions. Therefore, a combination of CUD3 for the convective derivatives in the constitutive equations and COM4 for the polymeric stress derivatives in the momentum equations is recommended to be used for numerical simulation of highly extensional flows.

• 한국해안해양공학회지
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• 제10권2호
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• pp.83-92
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• 1998

대격자망 수치모형에서 저항물체에 의한 유수저항을 평가하기 위하여, 항력으로부터 유도된 drag stress를 수심적분된 Reynolds 방정식에 도입하였다. 그리고, 해석해가 존재하는 조건에 대한 다양한 수치실험을 통하여 본 모형의 적용성 및 문제점을 검토하였다. 단일물체의 경우, 수치해는 해석해에 대하여 유속의 크기에 있어서$\pm$10% 정도의 오차범위를 나타내는 좋은 일치를 보였으며 후류폭의 크기도 전 경우에 있어서 해석해와 잘 일치 하였다. 또한, 열을 이룬 물체에 대한 항력계수와 와동점성계수가 정확하게 결정된다면, 본 모형은 열을 이룬 물체 배후에서 평균류의 흐름분포를 평가하는 데 효율적으로 이용될 수 있을 것이다.

• Structural Engineering and Mechanics
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• 제11권1호
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• pp.89-104
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• 2001

This paper reviews the author's work on the development of relationships between solutions of the Kirchhoff (classical thin) plate theory and the Mindlin (first order shear deformation) thick plate theory. The relationships for deflections, stress-resultants, buckling loads and natural frequencies enable one to obtain the Mindlin plate solutions from the well-known Kirchhoff plate solutions for the same problem without much tedious mathematics. Sample thick plate solutions, deduced from the relationships, are presented as benchmark solutions for researchers to use in checking their numerical thick plate solutions.