• 한국전산유체공학회지
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• 제13권3호
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• pp.69-78
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• 2008

The high-order numerical method based on the adaptive mesh refinement(AMR) on the quadrilateral unstructured grids has been developed in this paper. This adaptive-grid method, originally developed with MUSCL-TVD scheme, is now extended to the WENO (weighted essentially no-oscillatory) scheme with the Runge-Kutta time integration of fifth order in spatial and temporal accuracy. The multidimensional interpolation was studied in the preliminary research, which allows us to maintain the same order of accuracy for the computation of numerical flux between two adjacent cells of different levels. Some standard benchmark tests are done to validate this method for checking the overall capacity and efficiency of the present adaptive-grid technique.

• 한국전산유체공학회지
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• 제11권4호
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• pp.39-47
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• 2006

In this paper, the authors developed a multidimensional interpolation method inside a finite volume cell in the computation of high-order accurate numerical flux such as the fifth order WEND (weighted essentially non-oscillatory) scheme. This numerical method starts from a simple Taylor series expansion in a proper spatial order of accuracy, and the WEND filter is used for the reconstruction of sharp nonlinear waves like shocks in the compressible flow. Two kinds of interpolations are developed: one is for the cell-averaged values of conservative variables divided in one mother cell (Type 1), and the other is for the vertex values in the individual cells (Type 2). The result of the present study can be directly used to the cell refinement as well as the convective flux between finer and coarser cells in the Cartesian adaptive grid system (Type 1) and to the post-processing as well as the viscous flux in the Navier-Stokes equations on any types of structured and unstructured grids (Type 2).

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2006년도 추계 학술대회논문집
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• pp.47-50
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• 2006

In the aeroacoustic application of computational fluid dynamics, the physical phenomena like the crackle in the unsteady compressible jets should be based on very time-accurate numerical solution. The accuracy of the present numerical scheme is extended to the fifth order, using the WENO filter to the sixth-order central difference computation. However, the computational capacity is very restricted by the environment of computational power, so therefore the quadrilateral adaptive grids technique is introduced for this high-order accuracy scheme. The first problem is the multi-dimensional interpolation between fine and coarse grids. Some general benchmark problems are solved to show the effectiveness of this method.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2001년도 춘계 학술대회논문집
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• pp.93-98
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• 2001

An adaptive Cartesian grid method having the best elements of structured, unstructured, and Cartesian grids is developed to solve the steady two-dimensional Euler equations. The solver is based on a cell-centered finite-volume method with Roe's flux-difference splitting and implicit point Gauss-seidel time integration method. Calculations of several compressible flows are carried out to show the efficiency of the developed computer code. The results were generally in good agreements with existing data in the literature and the developed code has the good ability to capture important feature of the flows.

• 한국수자원학회논문집
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• 제36권4호
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• pp.705-713
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• 2003

본 연구에서는 근해 지진해일에 의한 원형섬 주변에서의 처오름높이를 산정하기 위하여 사면구조(quadtree) 격자기법을 이용한 수치모형을 개발하였다. 비선형 천수방정식을 지배방정식으로 사용하였으며, 적합화된 계층적 사면구조 격자를 이용하여 leap-frog 기법으로 양해적으로 유한차분하였다. 원형섬 주위를 따라 적용된 사면구조 격자는 사각형 및 원형의 형상으로 세밀화 되었다. 계산된 수치해석결과를 검증하기 위해 수리실험결과와 비교하였으며, 본 연구의 결과는 수리실험결과와 양호하게 일치하였다.

• 대한기계학회논문집
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• 제19권9호
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• pp.2237-2248
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• 1995

In incompressible flow which has multi-length scale, it has a very important effect which dependent variables are used for adaptive grid generation. Among many length scales in incompressible flow, the dependent variables used for the adaptive grid generation should be able to represent the feature of the concerned system. In this paper, by using vorticity and stream function, in addition to velocity components, the smoother and more stable grid generation is possible and these four flow properties represent each scale. The adaptive grid generation for a lid-driven cavity flow with $N_{re}$ =3200 using four flow properties such as velocity components, vorticity, stream function is performed, and the usefulness of using vorticity and stream function as the indicator for adaptive grid generation is shown.

• 한국방재학회 논문집
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• 제4권2호
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• pp.71-76
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• 2004

본 연구에서는 지진해일에 의한 원형섬 주변에서의 범람영역을 산정하기 위하여 사면구조(quadtree) 격자 기법을 이용한 수치모형을 개발하였다. 비선형 천수방정식을 지배방정식으로 사용하였으며, 적합화된 계층적사면구조 격자를 이용하여 leap-frog 기법으로 양해적으로 유한차분하였다. 원형섬 주위를 따라 적용된 사면구조 격자는 사각형 및 원형의 형상으로 세밀화 되었다. 본 모형에 의해 계산된 수치해석결과를 검증하기 위해 원형섬 주변의 처오름높이에 대한 수리실험결과와 비교하였으며, 본 연구의 결과는 수리실험결과와 양호하게 일치하였다.

• 한국전자파학회논문지
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• 제14권8호
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• pp.823-829
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• 2003

고주파용 마이크로스트립 선로의 모델링에 필수적인 인덕턴스의 빠른 추출을 위해서 고속화 알고리즘(fast mutilpole method)과 결합된 적응 PEEC 격자분할법(adaptive PEEC grid refinement algorithm)을 제안하였다. 격자의 세분화는 마이크로스트립 선로의 구조와 사용주파수에 따른 전류분포에 적합하도록 이루어졌는데, 이 적응 격자는 주로 전류분포가 높은 영역에서 더 세분화된다. 이 기법을 이용하여 마이크로스트립 선로의 인덕턴스를 구하였고, 계산결과는 빠르게 수렴하여 계산시간과 격자 수를 줄이는데 효율적임을 보였다.

• 대한수학회보
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• 제45권4호
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• pp.781-795
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• 2008

In this paper, we describe the application procedure of the adaptive mesh refinement (AMR) for the weighted essentially non-oscillatory schemes (WENO), and observe the effects of the derived algorithm when problems have piecewise smooth solutions containing discontinuities. We find numerically that the dissipation of the WENO scheme can be lessened by the implementation of AMR while the accuracy is maintained. We deduce from the experiments that the AMR-implemented WENO scheme captures shocks more efficiently than the WENO method using uniform grids.

• 한국전산유체공학회지
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• 제1권1호
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• pp.88-97
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• 1996

This paper treats an adaptive finite-element method for the viscous compressible flow governed by Navier-Stokes equations in two dimensions. The numerical algorithm is the two-step Taylor-Galerkin mettled using unstructured triangular grids. To increase accuracy and stability, combined moving node method and grid refinement method have been used for grid adaption. Validation of the present algorithm has been made by comparing the present computational results with the existing experimental data and other numerical solutions. Four benchmark problems are solved for demonstration of the present numerical approach. They include a subsonic flow over a flat plate, the Carter flat plate problem, a laminar shock-boundary layer interaction. and finally a laminar flow around NACA0012 airfoil at zero angle of attack and free stream Mach number of 0.85. The results indicates that the present adaptive triangular grid method is accurate and useful for laminar viscous flow calculations.