• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.7
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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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.7
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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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.7
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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 Korea Water Resources Association
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• v.38 no.2
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• pp.155-166
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• 2005

Upwind schemes are very well adapted to the discontinuous flow and have become popular for applications Involving dam break flow, transcritical Slow, etc. However, upwind schemes have been applied mainly to the idealized problems not to the natural channels with irregular geometry so far because of the error due to source terms. In this paper, the new type of upwind discretization of source terms, which uses the normalized Jacobian to discretize the source terms, is proposed. As results of tests to flows with source terms by the upwind models, the method proposed in this paper is proved as efficient and accurate. This generalized method for differencing source terms is simple and might beapplicable to diverse type of flux upwind discretization scheme in finite difference method.