• 대한기계학회논문집B
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• 제27권7호
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• pp.973-983
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• 2003

The suitability of high-order accurate, centered and upwind-biased compact difference schemes is evaluated for large eddy simulation of turbulent flow. Two turbulent flows are considered: turbulent channel flow at Re = 23000 and flow over a circular cylinder at Re = 3900. The effects of numerical dissipation on the finite differencing and aliasing errors and the subgrid-scale stress are investigated. It is shown through the simulations that compact upwind schemes are not suitable for LES, whereas the fourth order-compact centered scheme is a good candidate for LES provided that proper dealiasing of nonlinear terms is performed. The classical issue on the aliasing error and the treatment of nonlinear terms is revisited with compact difference schemes.

• 대한기계학회논문집B
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• 제27권7호
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• pp.995-1006
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• 2003

The suitability of high-order accurate, centered and upwind-biased compact difference schemes for large eddy simulation is evaluated by a dynamic analysis. Large eddy simulation of isotropic turbulence is performed with various dissipative and non-dissipative schemes to investigate the effect of numerical dissipation on the resolved solutions. It is shown by the present dynamic analysis that upwind schemes reduce the aliasing error and increase the finite differencing error. The existence of optimal upwind scheme that minimizes total numerical error is verified. It is also shown that the finite differencing error from numerical dissipation is the leading source of numerical errors by upwind schemes. Simulations of a turbulent channel flow are conducted to show the existence of the optimal upwind scheme.

• 대한기계학회논문집B
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• 제27권7호
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• pp.984-994
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• 2003

The suitability of high-order accurate, centered and upwind-biased compact difference schemes for large eddy simulation is evaluated by a spectral, static error analysis. To investigate the effect of numerical dissipation on LES solutions, power spectra of discretization errors are evaluated for isotropic turbulence models in both continuous and discrete wavevector spaces. Contrary to the common belief, the aliasing errors from upwind-biased schemes are larger than those from comparable non-dissipative schemes. However, this result is the direct consequence of the definition of the power spectral density of the aliasing error, which poses the limitation of the static error analysis for upwind schemes.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권2호
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• pp.75-81
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• 2003

Compact schemes are shown to be effective for a class of problems including convection-diffusion equations when combined with multigrid algorithms [7, 8] and V-cycle convergence is proved[5]. We apply the multigrid algorithm for an semianalytic finite difference scheme, which is desinged to preserve high order accuracy despite of singularities.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1998년도 추계 학술대회논문집
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• pp.7-12
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• 1998

Optimized high-order compact(OHOC) schemes were proposed, which have high spatial order of truncation and resolution to simulate the aeroacoustic problems due to unsteady compressible flows. Generally, numerical schemes are categorized explicit or implicit by time-marching method. In this research, OHOC differences which were developed with explicit time-marching method is used to have implicit formulation and the implicit OHOC differences result in block hepta-diagonal matrix. This paper presents the comparisons between the explicit and implicit OHOC schemes with a second order accuracy of time in the 1-d linear wave convection problem, and between the explicit OHOC scheme of 4th-order accuracy in time and the implicit OHOC scheme of 1st-order accuracy in tine for the 1-d nonlinear wave convection problem. With these comparisons, the characteristics of implicit OHOC scheme are shown in the point of CFL number.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.235-244
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• 2012

In this paper, we solve the three-dimensional biharmonic equation with Dirichlet boundary conditions of second kind using the full multigrid (FMG) algorithm. We derive a finite difference approximations for the biharmonic equation on a 18 point compact stencil. The unknown solution and its second derivatives are carried as unknowns at grid points. In the multigrid methods, we use a fourth order interpolation to producing a new intermediate unknown functions values on a finer grid, and the full weighting restriction operators to calculating the residuals at coarse grid points. A set of test problems gives excellent results.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1995년도 추계 학술대회논문집
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• pp.197-202
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• 1995

비정상(unsteady) 압축성(compressible) 유동에 의한 공력음향(aeroacoustics)을 모사하여 공력소음원을 해석하기 위해서는 고차(high order)의 정확도와 높은 해상도(resolution)를 가지며, 상대적으로 계산시간을 많이 필요로 하지 않는 외재적(explicit) 유한차분법이 필수적으로 요구된다. 이것은 주어진 차분방식과 격자계로써 공간과 시간상에 존재하는 미소크기의 파동성분들을 충분히 구현하여야 만족할 만한 수치해를 얻을 수 있기 때문이다. 본 연구에서는, 그러한 유한차분법 중 최근에 관심의 대상이 되고있는 삼각(tridiagonal)또는 오각(pentadiagonal) 집적유한차분법(compact finite difference scheme)이 최대의 해상도를 갖도록 하는 수학적인 방법을 개발하고, 이 방법으로써 새롭게 집적유한차분법을 최적화하였다. 개발된 최적화 방법은, 푸리에 해석법(Fourier analysis)을 통하여 파동수(wavenumber) 영역에서 수학적으로 계산된 위상오차(phase error)를 최소화하는 것이며, 이러한 개념과 방법은 본 연구에서 처음으로 집적유한차분법에 적용되었다. 여러가지 절단정확도(truncation order)에 대해서 최적화 된 집적유한차분법들이 실제 공간과 시간상에서 보여주는 정확도와 오차특성을 알아보기 위하여, 이 방법들을 1차원 선형파동방정식에 적용하였고, 이 결과를 통하여 가장 정확하고 효과적인 절단정확도의 집적유한차분법을 선별하였다. 특히, 오각(pentadiagonal)법에 비해 더욱 효율적인 6차 삼각(tridiagonal)법을 1차원 Euler방정식에 적용하여, 비선형 파동에 대한 모사를 수행할 수 있었다.