• 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.24 no.9
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• pp.1227-1238
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• 2000

This study examines the effects of the discretization schemes on numerical solutions of viscoelastic fluid flows. For this purpose, a temporally evolving mixing layer, a two-dimensional vortex pair interacting with a wall, and a turbulent channel flow are selected as the test cases. We adopt a fourth-order compact scheme (COM4) for polymeric stress derivatives in the momentum equations. For convective derivatives in the constitutive equations, the first-order upwind difference scheme (UD) and artificial diffusion scheme (AD), which are commonly used in the literature, show most stable and smooth solutions even for highly extensional flows. However, the stress fields are smeared too much and the flow fields are quite different from those obtained by higher-order upwind difference schemes for the same flow parameters. Among higher-order upwind difference schemes, a third-order compact upwind difference scheme (CUD3) shows most stable and accurate solutions. Therefore, a combination of CUD3 for the convective derivatives in the constitutive equations and COM4 for the polymeric stress derivatives in the momentum equations is recommended to be used for numerical simulation of highly extensional flows.

• 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.

• 한국전산유체공학회:학술대회논문집
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• 1997.10a
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• pp.99-105
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• 1997

A finite-difference method based on conservative supra characteristic method type upwind flux difference splitting has been developed to study the nonequilibrium chemically reacting inviscid flow. For nonequilibrium air, NS-1 species equations were strongly coupled with flowfield equations through convection and species production terms. Inviscid nonequilibrium chemically reacting air mixture flows over Blunt-body were solved to demonstrate the capability of the current method. At low altitude flight conditions the nonequilibrium air models predicted almost the same temperature, density and pressure behind the shock as equilibrium flow: however, at high altitudes they showed substantial differences due to nonequilibrium chemistry effect. The new nonequilibrium chemically reacting upwind flux difference splitting mettled can be extended to viscous flow and multi-dimensional flow conditions.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.78-83
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• 1998

A finite-difference method based on conservative supra characteristic method(CSCM) type upwind flux difference splitting has been studied on the bluntness effect on the wall heat transfer rate and wall pressure over blunt-body. The results show that the stagnation heating varies inversely with the square root of the nose radius.

• Journal of computational fluids engineering
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• v.4 no.1
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• pp.8-18
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• 1999

In devising a numerical approximation for the convective spatial transport of a fluid mechanical quantity, it is noted that the convective motion of a scalar quantity occurs in one-way, or from upstream to downstream. This consideration leads to a new scheme termed a pure upwind difference scheme (PUDS) in which an estimated value for a fluid mechanical quantity at a control surface is not influenced from downstream values. The formal accuracy of the proposed scheme is third order accurate. Two typical benchmark problems of a wall-driven fluid flow in a square cavity and a buoyancy-driven natural convection in a tall cavity are computed to evaluate performance of the proposed method. for comparison, the widely used simple upwind scheme, power-law scheme, and QUICK methods are also considered. Computation results are encouraging: the proposed PUDS sensitized to the convection direction produces the least numerical diffusion among tested convection schemes, and, notable improvements in representing recirculation of fluid stream and spatial change of a scalar. Although the formal accuracy of PUDS and QUICK are the same, the accuracy difference of approximately a single order is observed from the revealed results.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.807-810
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• 2002

The suitability of high-order accurate, central and upwind-biased compact difference schemes is evaluated for the large-eddy simulations of flows in complex geometry. Two flow geometries are considered: channel and circular cylinder. The effects of numerical dissipation and aliasing error on the evaluation of subgrid scale stress are investigated by extending the analysis by Ghosal (1) to centered and upwind compact schemes. It is shown that the failure of upwind schemes mainly comes from the aliasing error.

• 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
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• v.18 no.3
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• pp.653-661
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• 1994

In this paper the CSCM type upwind flux difference splitting Navier-Stokes method has been applied to study the ARL-SL19 supersonic/transonic compressor cascade flow. H-type grid was chosen for its simplicity in applying cyclic tridiagonal matrix algorithm along with conventional slip/no-slip boundary conditions. The thin-layer algebraic model of Baldwin-Lomax was employed for the calculation of turbulent flows. The test case inlet Mach No. was 1.612 and inlet/exit pressure ratio($P_2/P_1$) was 2.15. The results were compared with experimental results from current method were compared well in suction surface with the experiments and other computational results; however, not well in pressure surface. It might be due to the complex flowfields such as shock/boundary layer interaction, turbulence, and flow separation, etc. In the future, a proper turbulence modelling and adaptive grid system will be studied to improve the solution quality.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.2
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• pp.467-474
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• 1993

Viscous flow and heat transfer phenomena in an axisymmetric cylinder which models a diesel engine have been numerically studied. In order to search for a way to minimize numerical diffusion, the effectiveness and the appropriateness of two selected numerical schemes for convective terms in the governing equations have been tested. They are Linear Upwind Difference Scheme and Hybrid Scheme. Using a standard k-.epsilon. turbulence model, the calculation has been carried out basically up to 180.deg. of crank angle. As a result, it was shown from comparison with previous experimental data that Linear Upwind Difference Scheme is less influenced than Hybrid Scheme by the numerical diffusion and it was suggested that these effects of numerical diffusion can be more significant than those due to turbulence modeling.