High order finite differencing schemes and their accuracy for CFD

Yiqing Shen, GeCheng Zha

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

This paper investigates different high order finite difference schemes and their accuracy for Burgers equation and Navier-Stokes equations. On a coarse grid, theoretical and numerical analysis indicate that a higher order difference scheme does not necessarily obtain more accurate solutions than a lower order scheme in the regions of high gradient variation (2nd order derivative). On a coarse grid, the numerical experiments indicate that the 3rd order biased upwind differencing for the inviscid fluxes with 2nd order central differencing for viscous term outperforms all other schemes with the accuracy order as high as 7th order. For the linear Burgers equation, both the analytical and numerical results indicate that a higher order scheme will be more accurate than a lower order scheme only when ReΔx ≤ 1. For the nonlinear Burgers equation, the numerical experiments also show the same conclusion. A numerical solution of laminar wall boundary layer from Navier-Stokes equations shows the same observation that a lower order scheme is more accurate on a coarse grid. The conception that a high order scheme can reduce mesh size unconditionally may be incorrect. Since the discrepancy occurs mostly in the region with high gradient variation, the refined mesh should not only be near the wall surface where the gradient is high, but also near the edge of the boundary layer where the gradient variation is high. The mesh spacing criterion for Navier-Stokes equation that a higher order scheme will be more accurate than a lower order scheme is not obtained yet. Using the criterion of the linear Burgers equation for Navier-Stokes equations may be excessive and preventively expensive. To resolve a laminar wall boundary layer accurately, the recommended grid Reynolds number is to be below 25 across the boundary layer. However, this is the criterion from the numerical experiments for all the finite differencing schemes, not for the higher order schemes to have better accuracy.

Original languageEnglish
Title of host publication47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
StatePublished - Dec 1 2009
Event47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition - Orlando, FL, United States
Duration: Jan 5 2009Jan 8 2009

Other

Other47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
CountryUnited States
CityOrlando, FL
Period1/5/091/8/09

Fingerprint

Burger equation
Navier-Stokes equations
charge flow devices
Navier-Stokes equation
Navier Stokes equations
boundary layers
Computational fluid dynamics
Boundary layers
boundary layer
grids
mesh
gradients
experiment
Experiments
mesh size
Reynolds number
numerical analysis
Numerical analysis
spacing
Fluxes

ASJC Scopus subject areas

  • Space and Planetary Science
  • Aerospace Engineering

Cite this

Shen, Y., & Zha, G. (2009). High order finite differencing schemes and their accuracy for CFD. In 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition [2009-1137]

High order finite differencing schemes and their accuracy for CFD. / Shen, Yiqing; Zha, GeCheng.

47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. 2009. 2009-1137.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Shen, Y & Zha, G 2009, High order finite differencing schemes and their accuracy for CFD. in 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition., 2009-1137, 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, FL, United States, 1/5/09.
Shen Y, Zha G. High order finite differencing schemes and their accuracy for CFD. In 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. 2009. 2009-1137
Shen, Yiqing ; Zha, GeCheng. / High order finite differencing schemes and their accuracy for CFD. 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. 2009.
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