• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2000년도 추계 학술대회논문집
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• pp.129-134
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• 2000

An efficient numerical method to solve the unsteady incompressible Navier-Stokes equations is developed. A fully implicit time advancement is employed to avoid the CFL(Courant-Friedrichs-Lewy) restriction, where the Crank-Nicholson discretization is used for both the diffusion and convection terms. Based on a block LU decomposition, velocity-pressure decoupling is achieved in conjunction with the approximate factorization. Main emphasis is placed on the additional decoupling of the intermediate velocity components with only n th time step velocity The temporal second-order accuracy is Preserved with the approximate factorization without any modification of boundary conditions. Since the decoupled momentum equations are solved without iteration, the computational time is reduced significantly. The present decoupling method is validated by solving the turbulent minimal channel flow unit.

• 대한기계학회논문집
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• 제19권8호
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• pp.1950-1963
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• 1995

A modification of the approximate-factorization method is made to accelerate the convergency rate and to take sufficiently large Courant number without loss of accuracy. And a stable implicit finite-difference scheme for solving the incompressible Navier-Stokes equations employed above modified method is developed. In the present implicit scheme, the volume fluxes with contravariant velocity components and the pressure formulation in curvilinear coordinates is adopted. In order to satisfy the continuity condition completely and to remove spurious errors for the pressure, the Navier-Stokes equations are solved by a modified SMAC scheme using a staggered gird. The upstream-difference scheme such as the QUICK scheme is also employed to the right hand side. The implicit scheme is unconditionally stable and satisfies a diagonally dominant condition for scalar diagonal linear systems of implicit operator on the left hand side. Numerical results for some test calculations of the two-dimensional flow in a square cavity and over a backward-facing step are obtained using both usual approximate-factorization method and the modified one, and compared with each other. It is shown that the present scheme allows a sufficiently large Courant number of O(10$^{2}$) and reduces the computing time.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1999년도 추계 학술대회논문집
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• pp.17-22
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• 1999

Convergence characteristics and efficiency of three implicit approximate factorization schemes(ADI, DDADI and MAF) are examined using 2-Dimensional compressible upwind Navier-Stokes code. Second-order CSCM(Conservative Supra Characteristic Method) upwind flux difference splitting method with Fromm scheme is used for the right-hand side residual evaluation, while generally first-order upwind differencing is used for the implicit operator on the left-hand side. Convergence studies are performed using an example of the flow past a NACA0012 airfoil at steady transonic flow condition, i. e. Mach number 0.8 at $1.25^{\circ}$ angle of attack. The results were compared with other computational results in order to validate the current numerical analysis. The results from the implicit AF algorithms were compared well in low surface with the other computational results; however, not well in upper surface. It might be due to lack of the grid around the shock position. Because the algorithm minimizes the errors of the approximate decomposition, the improved convergence rate with MAF were observed.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.59-80
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• 2003

An incomplete factorization method for preconditioning symmetric positive definite matrices is introduced to solve normal equations. The normal equations are form to solve linear least squares problems. The procedure is based on a block incomplete Cholesky factorization and a multilevel recursive strategy with an approximate Schur complement matrix formed implicitly. A diagonal perturbation strategy is implemented to enhance factorization robustness. The factors obtained are used as a preconditioner for the conjugate gradient method. Numerical experiments are used to show the robustness and efficiency of this preconditioning technique, and to compare it with two other preconditioners.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2002년도 추계 학술대회논문집
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• pp.95-102
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• 2002

Studies of the numerical characteristics of implicit upwind schemes, such as upwind ADI, Line Gauss-Seidel(LGS) and Point Gauss-Seidel(LU) algorithms, for preconditioned Navier-Stokes equations ate performed. All the algorithms are expressed in approximate factorization form and Von Neumann stability analysis and convergence studies are made. Preconditioning is applied for efficient convergence at low Mach numbers and low Reynolds numbers. For high aspect ratio computations, the ADI and LGS algorithms show efficient and uniform convergence up to moderate aspect ratio if we adopt viscous preconditioning based on min- CFL/max- VNN time-step definition. The LU algorithm, on the other hand, shows serious deterioration in convergence rate as the grid aspect ratio increases. Computations for practical applications also verify these results.

• International Journal of Internet, Broadcasting and Communication
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• 제13권3호
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• pp.63-72
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• 2021

Mobile crowd-sensing (MCS) is a promising sensing paradigm that leverages mobile users with smart devices to perform large-scale sensing tasks in order to provide services to specific applications in various domains. However, MCS sensing tasks may not always be successfully completed or timely completed for various reasons, such as accidentally leaving the tasks incomplete by the users, asynchronous transmission, or connection errors. This results in missing sensing data at specific locations and times, which can degrade the performance of the applications and lead to serious casualties. Therefore, in this paper, we propose a missing data inference approach, called missing data approximation with probabilistic tensor factorization (MDI-PTF), to approximate the missing values as closely as possible to the actual values while taking asynchronous data transmission time and different sensing locations of the mobile users into account. The proposed method first normalizes the data to limit the range of the possible values. Next, a probabilistic model of tensor factorization is formulated, and finally, the data are approximated using the gradient descent method. The performance of the proposed algorithm is verified by conducting simulations under various situations using different datasets.

• 대한조선학회논문집
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• 제31권1호
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• pp.63-70
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• 1994

항공유체의 계산에 주로 사용되는 음해법의 하나인 IAF(Implicit Approximate Factorization)법을 이용해 3차원 Wigley 선형 주위의 자유표면파 및 점성유동장을 해석하였다. IAF 법을 사용함으로서 기존 Euler 양해법의 계산 시간을 50% 이상 감소시키는데 성공하였다. 수치기법으로 국부선형화와 Euler 음해법을 사용하였으며 artificial viscosity의 생성을 위한 압력 구배항은 사용하지 않았다. 수치 계산은 Reynolds 수 $10^6$. Froude 수 0.25, 0.289 및 0.316에 대하여 수행하였고 난류 모형으로는 Baldwin-Lomax 모형을 사용하였으며 주요 계산 결과로는 자유표면화 형상 및 속도분포 등이었다. 본 연구에서는 그 중에서 자유표면파 형상에 대한 계산 결과를 실험값 및 Euler 양해법을 사용한 결과와 각각 비교 검토하였다.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2003년도 춘계공동학술대회
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• pp.386-393
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• 2003

For fast Cholesky factorization, it is most important to reduce the number of non-zero elements by ordering methods. Minimum deficiency ordering produces less non-zero elements. However, since it is very slow. the minimum degree algorithm is widely used. To improve the computation time, Rothberg's AMF uses an approximate deficiency instead of computing the deficiency. In this paper we present simple efficient methods to obtain a good approximate deficiency using information related to cliques. Experimental results show that our proposed method produces better ordering quality than that of AMF.

• 대한토목학회논문집
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• 제31권3B호
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• pp.293-303
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• 2011

비압축성 점성 흐름을 수치해석하기 위한 효율적인 대각행렬화된 근사 인수분해(DAF) 알고리즘을 개발하였다. 압력에 근거한 인공압축성(AC) 기법을 이용하여 3차원 정상 비압축성 Navier-Stokes 방정식을 계산한다. AC 형태로 변형된 지배방정식은 2차 정확도의 유한차분법을 이용하여 공간에 대해서 이산화하였다. 이산화된 방정식계를 2차 정확도로 분할하기 위해서 본 연구에서 개발한 DAF 기법을 적용한다. 이 연구의 목적은 이 DAF 기법의 계산상 효율성을 검토하는 것이다. 만곡부를 갖는 사각형 덕트에서 완전히 발달한 층류 흐름과 발달하는 층류흐름 그리고 공동에서의 층류흐름에 대한 DAF 기법의 해석결과를 잘 알려진 4단계 Runge-Kutta(RK4)기법에 의한 해석해와 상대적으로 비교평가 하였다. 공간에 대해서 동일한 이산화기법을 이용하므로 동일한 격자상에서 계산된 DAF기법과 RK4기법의 해는 근본적으로 동일한 반면에, 이들 두기법의 계산상 효율성은 확연히 다른 것으로 나타났다. 본 연구에서 개발된 DAF기법은 적용한 모든 흐름 문제에 대해서 RK4기법에 비해 최소 2배 이상 적은 계산 시간만을 필요로 하는 것으로 나타났다. 이러한 DAF 기법의 계산상 효율성은 계산용량의 추가나 프로그래밍의 추가적인 복잡함이 없이 확보된다.

• 에너지공학
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• 제9권4호
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• pp.309-318
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• 2000

핀-관 열교환기의 효율을 증대시키기 위하여는 열저항을 결정하는 데 있어서 중요한 역할을 하는 공기측 열전달 특성의 향상이 필요하다. 본 연구에서는 핀-관 열교환기의 공리측 성능을 해석하기 위해서 3차원 비압축성 Navier-Stokes 코드를 개발하였으며 이 코드는 시간항에 스칼라 내재적 근사분해법(scalar implicit approximate factorization)절차, 공간항에 유한체적법과 2차의 풍상차분법(upwind differencing)을 사용한다. 서로 다른 3개의 핀형상(평판핀, 슬릿핀, 파형핀)을 고려하였고 이들의 유동 및 열전달 특성을 연구하였다.