• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2004년도 학술대회지
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• pp.216-221
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• 2004

In two dimensional incompressible flaws, a preconditioning technique called Hierarchical Iterative Procedure(HIP) has been implemented on a SUPG finite element formulation. By using the SUPG formulation, one can escape from the LBB constraint and hence achieve an equal order formulation. In this paper, we increased the order of interpolation up to cubic. The conjugate gradient squared(CGS) method is used for the outer iteration, and the HIP for the preconditioning for the incompressible Navier-Stokes equation. The hierarchical elements has been used to achieve a higher order accuracy in fluid flaw analyses, but a proper efficient iterative procedure for higher order finite element formulation has not been available so far. The numerical results by the present HIP for the lid driven cavity flaw showed the present procedure to be stable, very efficient and useful in flaw analyses in conjunction with hierarchical elements.

• 한국전산유체공학회지
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• 제13권4호
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• pp.13-23
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• 2008

This paper is an extension of previous study[1] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite (serendipity) cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires four degrees-of-freedom at each element corners. Those degrees-of-freedom are the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational basis functions from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[2].

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 학술대회
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• pp.33-41
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• 2008

This paper is an extension of previous study[9] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite serendipity cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires at each element corners four degrees-of-freedom such as the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational bases from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[7].

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년 추계학술대회논문집
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• pp.33-41
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• 2008

This paper is an extension of previous study[9] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite serendipity cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires at each element corners four degrees-of-freedom such as the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational bases from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[7].

• 대한수학회지
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• 제50권5호
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• pp.1129-1163
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• 2013

Based on finite element discretization, two linearization approaches to the defect-correction method for the steady incompressible Navier-Stokes equations are discussed and investigated. By applying $m$ times of Newton and Picard iterations to solve an artificial viscosity stabilized nonlinear Navier-Stokes problem, respectively, and then correcting the solution by solving a linear problem, two linearized defect-correction algorithms are proposed and analyzed. Error estimates with respect to the mesh size $h$, the kinematic viscosity ${\nu}$, the stability factor ${\alpha}$ and the number of nonlinear iterations $m$ for the discrete solution are derived for the linearized one-step defect-correction algorithms. Efficient stopping criteria for the nonlinear iterations are derived. The influence of the linearizations on the accuracy of the approximate solutions are also investigated. Finally, numerical experiments on a problem with known analytical solution, the lid-driven cavity flow, and the flow over a backward-facing step are performed to verify the theoretical results and demonstrate the effectiveness of the proposed defect-correction algorithms.

• 한국전산유체공학회지
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• 제10권2호
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• pp.38-47
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• 2005

Substructuring methods are often used in finite element structural analyses. In this study a multi-level substructuring(MLSS) algorithm is developed and proposed as a possible candidate for finite element fluid solvers. The present algorithm consists of four stages such as a gathering, a condensing, a solving and a scattering stage. At each level, a predetermined number of elements are gathered and condensed to form an element of higher level. At the highest level, each sub-domain consists of only one super-element. Thus, the inversion process of a stiffness matrix associated with internal degrees of freedom of each sub-domain has been replaced by a sequential static condensation of gathered element matrices. The global algebraic system arising from the assembly of each sub-domain matrices is solved using a well-known iterative solver such as the conjugare gradient(CG) or the conjugate gradient squared(CGS) method. A time comparison with CG has been performed on a 2-D Poisson problem. With one domain the computing time by MLSS is comparable with that by CG up to about 260,000 d.o.f. For 263,169 d.o.f using 8 x 8 sub-domains, the time by MLSS is reduced to a value less than $30\%$ of that by CG. The lid-driven cavity problem has been solved for Re = 3200 using the element interpolation degree(Deg.) up to cubic. in this case, preconditioning techniques usually accompanied by iterative solvers are not needed. Finite element formulation for the incompressible flow has been stabilized by a modified residual procedure proposed by Ilinca et al.[9].

• 대한의용생체공학회:의공학회지
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• 제20권1호
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• pp.29-36
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• 1999

본 연구는 목적은 PIV 시스템을 이용하여 분기관내 유동현상을 가시화하여 분기부 영역의 유동특성을 분석하는데 있다. PIV 시스템으로 유동장을 가시화하기 위해서 분기관 모델은 투명 아크릴판으로 제작하였고 작동유체와 추적입자는 각각 물과 송화가루를 사용하였다. 유동장에서 획득된 영상으로부터 속도벡터를 얻기 위해서 입자추적방법의 1-프레임 법과 2-프레임 법, 상호상관 PIV법인 2-프레임법을 사용하였다. PIV 시스템으로 측정된 실험결과의 신뢰성을 확보하기 위해서 표면구동 캐비티 유동의 속도분포를 4-프레임법으로 얻어진 기준 실험 데이터와 비교하였다. 분기관에서 뉴턴유체의 유동현상을 효과적으로 가시화하는데 필요한 상호상관 PIV방법의 2-프레임법을 적용하는 알고리즘을 개발하였고, sub-pixel과 면적보간을 사용하여 오벡터를 제거후 최종속도벡터를 얻었다. PIV를 이용한 분기관내 유동가시와 실험결과를 신뢰할 수 있는 수치해석 결과를 이용하여 검증한 결과 PIV 실험으로 얻어진 속도벡터는 수치해석의 결과와 잘 일치하였다. PIV 실험과 수치해석 결과로부터 분기관모델의 분기점 원위부에 재순환영역이 형성됨이 확인되었고 두 다른 방법을 이용한 재순환영역의 길이와 높이는 거의 동일하였다.

• 한국수자원학회논문집
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• 제47권6호
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• pp.537-546
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• 2014

홍수시 하천의 유속을 효율적이고 안전하게 측정할 수 있는 방법의 하나로 제시된 것이 표면 영상 유속 측정법이다. 일반적인 표면영상유속계(SIV)는 두장의 정지영상에서 영상 조각을 잘라낸 뒤 여기에 상호상관법을 적용하여 유속을 산정한다. 이 방법은 짧은 시간간격의 유속분포 측정에 매우 효율적이다. 그러나 장시간의 평균 유속장을 산정하는 데는 많은 시간이 소요되며, 순간 유속장을 산정하기 때문에 흐름 조건이나 촬영 조건에 따라 생기는 잡음이나 불확실성의 영향을 많이 받게 된다. 이를 개선하고자 개발된 방법이 시공간 영상을 이용하여 일정 시간동안의 유속의 평균을 한번에 산정하는 시공간영상유속계측법(STIV)이다. 시공간영상유속계측법 중의 하나인 휘도경사텐서법은 일정 시간동안의 시공간 영상을 한 번에 분석하기 때문에, 유속 산정 시간을 획기적으로 줄일 수 있는 장점이 있다. 그러나 이 방법은 하천의 일방향 유속만을 계산할 수 있기 때문에 구조물 주변이나 만곡이 있는 경우의 2차원 흐름 측정은 불가능하다는 한계가 있다. 이를 개선하기 위해서 본 연구에서는 상호상관법을 이용하여 2차원적으로 시공간 영상을 분석하는 방법(상호상관 시공간영상유속계측법)을 개발하였다. 이 방법은 시공간영상에서 시간축 방향으로 상관분석을 통해 영상변위를 산정하는 방법이다. 기존의 시공간영상분석기법 중 하나인 휘도경사텐서법이 주흐름 방향만 분석이 가능하였던 데 비하여, 상호상관 시공간 영상분석법은 2차원 유속분포 측정이 가능하고, 시간적인 평균을 취하기 때문에, 공간 해상도가 높으며, 전체적인 유속 분석시간이 매우 짧아지는 장점이 있다. 또한 공동 흐름에 대한 인공 영상을 이용한 오차 분석결과 최대 10% 이내, 평균적으로 5% 이하의 오차를 보여 상당히 정확하게 2차원 유속분포 측정이 가능한 것으로 나타났다.