• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2001년도 춘계 학술대회논문집
• /
• pp.189-194
• /
• 2001

In this paper, non-reacting and reacting flowfields were computed using a preconditioned Navier-Stokes solver. The preconditioning technique of Merkle et al. and TVD scheme or Chakravarthy and Osher was employed and the results obtained using developed code have a good agreement with the previous results and experimental data. The preconditioned Wavier-Stokes equation set with low Reynolds number $\kappa-\epsilon$ equation and species continuity equations, are discretized with strongly implicit manner and time integrated with LU-SSOR scheme. For the purpose of treating unsteady problem the duel-time stepping scheme was employed. For the validation of the code in incompressible flow regime, steady driven square cavity flow was considered and calculation result shows reasonably good agreement with the result of incompressible code. Shock wave/boundary layer interaction problem was considered to show the shock capturing performance of preconditioned-TVD scheme. To validate unsteady flow, acoustic oscillation problem was calculated, and supersonic premix flame of $H_2$-air reaction problem which is calculated with turbulence model, 9-species/18-reaction step reaction model, shows reasonable agreement with the previous results. As a result, the preconditioning method has an advantage to calculate incompressible and compressible flow through one code and preconditioned solver easily developed from standard compressible code with minor efforts. But additional computational time and computer memory is required due to preconditioning matrix.

• 한국항공우주학회지
• /
• 제36권2호
• /
• pp.115-122
• /
• 2008

예조건화 오일러 방정식의 수렴 특성에 미치는 특성 조건수의 영향을 조사하였다. 그리고 Choi와 Merkle 예조건화를 적용한 경우와 온도 예조건화를 적용한 경우의 수렴 특성을 분석하였다. 공간차분을 위해 예조건화 Roe의 FDS 기법을 적용하였고, 시간적분을 위해 예조건화 LU-SGS 기법을 적용하였다. 지배방정식의 수렴 특성은 특성 조건수에 크게 영향을 받는 것으로 나타났으며, 최적의 특성 조건수가 존재하는 것으로 나타났다. 그리고 최적의 특성 조건수는 Choi 와 Merkle 예조건화를 적용한 경우와 온도 예조건화를 적용한 경우가 서로 다른 것으로 나타났다.

• 한국항공우주학회지
• /
• 제36권2호
• /
• pp.123-130
• /
• 2008

예조건화 나비어스톡스 방정식의 수렴 특성에 미치는 특성 조건수의 영향을 조사하였다. Choi와 Merkle 예조건화를 적용한 경우와 온도 예조건화를 적용한 경우의 수렴 특성을 분석하였다. 공간차분을 위해 예조건화 Roe의 FDS 기법을 적용하였고, 시간적분을 위해 LU-SGS 기법을 적용하였다. 나비어스톡스 방정식의 수렴 특성은 특성 조건수에 크게 영향을 받으며, 최적의 특성 조건수가 존재하는 것을 보였다. 그리고 점성 유동의 최적 특성 조건수는 비점성 유동에 비해 큰 것으로 나타났다.

• Journal of applied mathematics & informatics
• /
• 제9권1호
• /
• pp.331-339
• /
• 2002

A preconditioned conjugate gradient(PCG) scheme with the aid of deflation for computing a few of the smallest eigenvalues arid their corresponding eigenvectors of the large generalized eigenproblems is considered. Topically there are two types of deflation techniques, the deflation with partial shifts and an arthogonal deflation. The efficient way of determining partial shifts is suggested and the deflation-PCG schemes with various partial shifts are investigated. Comparisons of theme schemes are made with orthogonal deflation-PCG, and their asymptotic behaviors with restart operation are also discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제3권1호
• /
• pp.99-106
• /
• 1999

An accelerated optimization technique combined with a stepwise deflation procedure is presented for the efficient evaluation of a few of the smallest eigenvalues and their corresponding eigenvectors of the generalized eigenproblems. The optimization is performed on the Rayleigh quotient of the deflated matrices by the aid of a preconditioned conjugate gradient scheme with the incomplete Cholesky factorization.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2002년도 춘계 학술대회논문집
• /
• pp.59-64
• /
• 2002

In this paper, the preconditioned multistage time stepping methods which are popular multigrid smoothers is implemented for the compressible Navier-Stokes calculation with full-coarsening multigrid method. The convergence characteristic of the point-Jacobi and Alternating direction line Jacobi(DDADI) preconditioners are studied. The performance of 2nd order upwind numerical fluxes such as 2nd order upwind TVD scheme and MUSCL-type linear reconstruction scheme are compared in the inviscid and viscous turbulent flow caculations.

• 한국연소학회:학술대회논문집
• /
• 한국연소학회 1999년도 제19회 KOSCO SYMPOSIUM 논문집
• /
• pp.219-230
• /
• 1999

The Equations of Chemical kinetics are very stiff, which forces the use of an implicit scheme. The problem of implicit scheme, however, is that the jacobian must be solved at each time step. In this paper, we examined the methodology that can be stable without full chemical jacobian, This method is derived by applying the different time steps to the chemical source term. And the lower triangular chemical jacobian is derived. This is called the preconditioned time differencing method and represents partial implicit method. We show that this method is more stable in chemical kinetics than the full implicit method and that this is more efficient in supersonic combustion problem than the full jacobian method with same accuracy.

• Journal of applied mathematics & informatics
• /
• 제22권1_2호
• /
• pp.467-474
• /
• 2006

We present and study the stability and convergence of a deflation-preconditioned conjugate gradient(PCG) scheme for the interior generalized eigenvalue problem $Ax = {\lambda}Bx$, where A and B are large sparse symmetric positive definite matrices. Numerical experiments are also presented to support our theoretical results.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제5권2호
• /
• pp.17-23
• /
• 2001

The evaluation of a few of the smallest eigenpairs of large symmetric eigenvalue problem is of great interest in many physical and engineering applications. A deflation-preconditioned conjugate gradient(PCG) scheme for a such problem has been shown to be very efficient. In the present paper we provide the numerical stability of a deflation-PCG with partial shifts.

• 한국추진공학회지
• /
• 제8권1호
• /
• pp.27-37
• /
• 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.