• International Journal of Aeronautical and Space Sciences
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• 제2권1호
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• pp.1-11
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• 2001

The time implicit point SGS scheme is applied to compute hypersonic viscous flows in thermochemical nonequilibrium. The performance of the point SGS scheme is then compared with those of the line SGS and the LU-SGS schemes. Comparison of convergence histories with the effect of multiple forward and backward sweeps are made for the flow over a 2D cylinder experimentally studied by Hornung and the flow over a hemisphere at conditions corresponding to the peak heating condition during the reentry flight of an SSTO vehicle. Results indicate that the point SGS scheme with multiple sweeps is as robust and efficient as the line SGS scheme. For the point SGS and the LU-SGS scheme, the rate of improvement in convergence is largest with two sweep cycles. However, for the line SGS scheme, it is found that more than one sweep cycle deteriorates the convergence rate.

• 한국전산유체공학회지
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• 제9권3호
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• pp.26-38
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• 2004

A study has been made for the investigation of the robustness and convergence of various implicit operators of the LU-SGS scheme using linear stability analysis. It is shown that the behavior of the implicit operator is not determined by its own characteristics, but is determined relatively depending on the dissipative property of the explicit operator. It is also shown that, as the dissipation level of the implicit operator increases, the robustness of the scheme increases, but the convergence rate can be deteriorated due to the excessive dissipation. The numerical results demonstrate that the dissipation level of the impliict operator needs to be higher than that of the explicit operator for computing stiff problems.

• 대한기계학회논문집B
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• 제23권1호
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• pp.82-91
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• 1999

A numerical analysis based on the three-dimensional Reynolds-averaged Navier-Stokes equation has been conducted to investigate the flow within a NASA rotor 67 transonic fan. General coordinate transformations are used to represent the complex blade geometry and an H-type grid is used. The governing equations are solved using implicit LU-SGS scheme for the time-marching integration and a standard ${\kappa}-{\varepsilon}$ model is used with wall functions for the turbulence modeling. The computations are compared with the experimental data and a detailed study of the flow structures near peak efficiency and near stall is presented. The calculated overall aerodynamic efficiency and three-dimensional shock system agree well with the laser anemometer data.

• 한국전산유체공학회지
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• 제9권3호
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• pp.39-48
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• 2004

In the present study, an efficient implementation technique of the van Leer's implicit operator is suggested in accordance with the Roe's explicit operator. By using an efficient treatment of the off-diagonal terms, which occupy most of the memory requirement for the linear system of equations, it is shown that the improved scheme only requires less than 30% of memory and is approximately 10-20% faster than the baseline scheme.

• 한국전산유체공학회지
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• 제19권1호
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• pp.27-33
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• 2014

A new and efficient implicit scheme is proposed to obtain a steady-state solution in time integration and the comparison of characteristics with the approximation ways for the implicit method to solve the incompressible Navier-Stokes equations is provided. The conservative, finite-volume cell-vertex upwind scheme and artificial compressibility method using dual time stepping for time accuracy is applied in this paper. The numerical results obtained indicate that the direct application of Jacobian matrix to the Lower and upper sweeps of implicit LU-SGS leads to better performance as well as convergence regardless of CFL number and true time step than explicit scheme and approximation of Jacobian matrix. The flow simulation around box in uniform flow with unstructured meshes is demonstrated to check the validity of the current formulation.

• International Journal of Aeronautical and Space Sciences
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• 제14권2호
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• pp.112-121
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• 2013

An approach for composing a performance optimized computational code is suggested for the latest microprocessors. The concept of the code optimization, termed localization, is maximizing the utilization of the second level cache that is common to all the latest computer systems, and minimizing the access to system main memory. In this study, the localized optimization of the LU-SGS (Lower-Upper Symmetric Gauss-Seidel) code for the solution of fluid dynamic equations was carried out in three different levels and tested for several different microprocessor architectures widely used these days. The test results of localized optimization showed a remarkable performance gain of more than two times faster solution than the baseline algorithm for producing exactly the same solution on the same computer system.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2001년도 춘계 학술대회논문집
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• pp.45-50
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• 2001

An approach of composing a performance optimized computational code is suggested for latest microprocessors. The approach named as localization is a concept of minimizing the access to system's main memory and maximizing the utilization of second level cache that is common to all the latest computer system. The localized compositions of LU-SGS scheme for fluid dynamics were made in three different levels and tested on three different microprocessor architectures most widely used in these days. The test results of localization concept showed a remarkable performance, that is the showing gain up to 4.5 times faster solution than the baseline algorithm $450\%$ for producing an exactly the same solution.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2001년도 춘계 학술대회논문집
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• pp.38-44
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• 2001

An efficient Gauss-Seidel time integration scheme is developed for solving the Euler and Navier-Stokes equations on unstructured meshes. Roe's FDS is used for the explicit residual computations and van Leer's FVS for evaluating implicit flux Jacobian. To reduce the memory requirement to a minimum level, off-diagonal flux Jacobian contributions are repeatedly calculated during the Gauss-Seidel sub-iteration process. Computational results based on the present scheme show that approximately $15\%$ of CPU time reduction is achieved while maintaining the memory requirement level to $50-60\%$ of the original Gauss-Seidel scheme.

• 한국항공우주학회지
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• 제30권7호
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• pp.68-80
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• 2002

최신 마이크로프로세서에서 성능 최적화된 수치 코드를 작성하는 접근법을 제시하였다. 국소화로 지칭한 이 코드 최적화 방법은 모든 최신 마이크로프로세서에서 채용되는 2차 캐시의 사용을 최대화하고 시스템의 주기억장치에 대한 접근을 최소화하는 개념이다. 본 연구에서는 유체역학 문제의 해결을 위한 LU-SGS 해법을 3 단계에 걸쳐 국소화 하였으며, 요즈음 널리 이용되고 있는 여러 가지 마이크로프로세서들에 대해 시험을 수행하였다. 국소 최적화 개념의 시험 결과는, 컴퓨터 시스템에 따라서는, 같은 컴퓨터에서 완전히 동일한 해를 기본 알고리즘에 비해 7.35배까지 빨리 얻을 수 있는 주목할 만한 성능을 보여 주었다.

• 한국추진공학회지
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• 제8권1호
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• pp.27-37
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• 2004

예조건화된 오일러 방정식의 수렴특성에 대한 연구를 수행하였다. 지배방정식의 거동을 이해하기 위하여 섭동 해석을 수행하였다. 중앙부에 10％ 원호를 가진 2차원 관을 통과하는 다양한 마하수의 비점성 유동장에 대해 수치 계산을 수행하였다. 공간차분은 Roe의 FDS를 사용하고 시간적분은 LU-SGS 기법을 사용하였다. 압력 및 속도의 수렴특성은 마하수와 상관없이 일정하게 유지되었으나, 온도의 수렴성은 마하수가 작아질수록 악화되는 것으로 나타났다. 섭동 해석을 통해 이러한 지배방정식의 수렴특성을 설명할 수 있었으며, 수렴특성이 예조건화 행렬의 거동 특성에 의해 결정된다는 사실을 알 수 있었다.