Critical Comparison of the Collocated and Staggered Grid Arrangements for Incompressible Turbulent Flows
TEXAS UNIV AT ARLINGTON DEPT OF MECHANICAL AND AEROSPACE ENGINEERING
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The collocated-mesh scheme is often favored over the staggered-mesh scheme for turbulence simulation in complex geometries due to its slightly simpler form in curvilinear coordinates. The collocated mesh scheme does not conserve kinetic energy however, and few careful checks of the impact of these errors have been made. In this work, analysis is used to identify two sources of kinetic energy conservation error in the collocated-mesh scheme 1 interpolation errors arising from second-order linear interpolation and 2 pressure errors. It is shown that the interpolation error can be eliminated through the use of a first-order accurate centered interpolation operator with mesh-independent weights. The pressure error can not be eliminated and it is shown to scale as OmicronDelta t exp 2Delta xexp 2. The effects of the conservation errors is investigated numerically by performing simulations of turbulent channel flow as well as inviscid simulations of the flow over an airfoil. The channel flow results are compared with those of a staggered-mesh code. Neither the second-order interpolation error nor the pressure error appear to lead to significant error in the channel where the Cartesian mesh is stretched in only one direction. The airfoil simulations performed in curvilinear coordinates show a much greater sensitivity to the interpolation errors. The second-order centered interpolation lead to severe numerical oscillations, while the kinetic energy-conserving first-order centered interpolation produce solutions that are almost as smooth as those obtained with a second-order upwind interpolation. These results suggest that numerical oscillations can be controlled in curvilinear coordinates through the use of properly-constructed non-dissipative centered interpolations.
- Fluid Mechanics