• Journal of computational fluids engineering
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• v.5 no.2
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• pp.47-54
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• 2000

A robust Navier-Stokes code has been developed to efficiently predict hypersonic flows in chemical nonequilibrium. The HLLE+ flux discretization scheme is used to improve accuracy and robustness of hypersonic flow analysis. An efficient LU approximate factorization method is also used to solve the flow equations and species continuity equations in fully coupled fashion to implicitly treat stiff source terms of chemical reactions. The HLLE+ scheme shows lower grid dependency for the wall heating rates than other schemes. The developed code has been used to compute chemical nonequilibrium air flow through expanding hypersonic nozzle and past two and three dimensional blunt-nosed bodies. The results are in good agreement with existing numerical and experimental results.

• 한국전산유체공학회:학술대회논문집
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• 1996.05a
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• pp.131-136
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• 1996

The numerical method for the flow field of a gas atomization process is presented. For the analysis of the compressible supersonic jet flow of a gas. an axisymmetric Navier-Stokes equations are solved using a LU-factored upwind method. The MUSCL type TVD scheme is used for the discretization of inviscid flux, whereas Steger-Warming splitting and LU factorization is applied to the implicit operator. For the validation of the present method, we computed the flow field around the simple gas atomizer proposed by Issac. The numerical results has shown excellent agreement with the experimental data.

• 한국전산유체공학회:학술대회논문집
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• 2000.10a
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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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1998.10a
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• pp.63-66
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• 1998

In the implementation of the simplex method program, the representation and the maintenance of basis matrix is very important, In the experimental study, we investigates Suhl's idea in the LU factorization and LU update of basis matrix. First, the triangularization of basis matrix is implemented and its efficiency is shown. Second, various technique in the dynamic Markowitz's ordering and threshold pivoting are presented. Third, modified Forrest-Tomlin LU update method exploiting sparsity is presented. Fourth, as a storage scheme of LU factors, Gustavson data structure is explained. Fifth, efficient timing of reinversion is developed. Finally, we show that modified Forrest-Tomlin method with Gustavson data structure is superior more than 30% to the Reid method with linked list data structure.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.8
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• pp.1122-1133
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• 2003

Numerical characteristics of implicit upwind schemes, such as upwind ADI, line Gauss-Seidel (LGS) and point Gauss-Seidel (LU) algorithms, for Navier-Stokes equations have been investigated. Time-derivative preconditioning method was applied for efficient convergence at low Mach/Reynolds number regime as well as at large grid aspect ratios. All the algorithms were expressed in approximate factorization form and von Neumann stability analysis was performed to identify stability characteristics of the above algorithms in the presence of high grid aspect ratios. Stability analysis showed that for high aspect ratio computations, the ADI and LGS algorithms showed efficient damping effect 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, showed serious deterioration in stability characteristics as the grid aspect ratio increases. Computations for several practical applications also verified these results.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.283-296
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• 2005

It is well known that the ordering of the unknowns can have a significant effect on the convergence of a preconditioned iterative method and on its implementation on a parallel computer. To do so, we introduce a block red-black coloring to increase the degree of parallelism in the application of the block ILU preconditioner for solving sparse matrices, arising from convection-diffusion equations discretized using the finite difference scheme (five-point operator). We study the preconditioned PGMRES iterative method for solving these linear systems.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.10
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• pp.1317-1325
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• 2000

A new efficient numerical method for computing three-dimensional, unsteady, incompressible flows is presented. To eliminate the restriction of CFL condition, a fully-implicit time advancement in which the Crank-Nicolson method is used for both the diffusion and convection terms, is adopted. Based on an approximate block LU decomposition method, the velocity -pressure decoupling is achieved. The additional decoupling of the intermediate velocity components in the convection term is made for the fully -implicit time advancement scheme. Since the iterative procedures for the momentum equations are not required, the velocity components decouplings bring forth the reduction of computational cost. The second-order accuracy in time of the present numerical algorithm is ascertained by computing decaying vortices. The present decoupling method is applied to minimal channel flow unit with DNS (Direct Numerical Simulation).

• Journal of KIISE:Computer Systems and Theory
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• v.28 no.5
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• pp.228-235
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• 2001

본 논문에서는 분산메모리를 가진 병렬 컴퓨터에서 밀집 행렬 연산을 위한 PoLAPACK 패키지를 소개한다. PoLAPACK은 새로운 연산 기법을 적용한 LU, QR, Cholesky 인수분해 알고리즘들을 포함하고 있다. 블록순환분산법으로 분산되어 있는 행렬에 알고리즘적인 블록 기법(algorithimic blocking)을 적용하여, 실제 행렬의 분산에 사용된 블록의 크기와 다른, 최대의 성능을 보일 수 있는 최적의 블록 크기로 연산을 수행할 수 있다. 이러한 연산 방식은 분산되어 있는 원래의 행렬 A의 순서를 따르지 않으며, 따라서 최적의 블록 크기로 연산을 수행한 후에 얻어진 해 x를 원래 행렬 분산법을 따라서 재배치하여야 한다. 본 연구는 Cray T3E 컴퓨터에서 구현하였으며 ScaLAPACK의 인수분해 루틴들과 그 성능을 비교.분석하였다.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.50 no.4
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• pp.166-171
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• 2001

Object-oriented programming is a solution for problems in the development, maintenance, and update of large software such as power system analysis software. However, many applications in the electrical industry critically depend on the computational efficiency of the implementation. In order to be flexible and reduce the computation time, this paper represents an efficient method for constructing a Jacobian matrix and for factorizing it, and designs the class hierarchy for power system. This method is applied to four different power systems for load flow calculation. The performance of the object-oriented program developed in C++ is assessed in computer simulation.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.8
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• pp.917-923
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• 1999

This paper proposes an efficient method of hydro-thermal scheduling in coordination with head variation and hydraulically coupled plants using Evolutionary Programing(EP). Based on the EP technique, the proposed algorithm is capable of determining the global optimal solutions. The constraints such a power balance condition, water available condition and transmission losses are embedded and satisfied throughout the proposed EP approach. The effectiveness of the proposed approach is demonstrated on the test systems and compared to those of other method. The results show that the new approach obtains a more highly optimal solutions than the conventional other methods such as newton-raphson method, Dynamic Programming(DP), LU factorization.