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Second Symposium on Turbulence and Shear Flow Phenomena
June, 27-29, 2001, KTH, Stockholm, Sweden

DOI: 10.1615/TSFP2

A NEW METHOD FOR DIRECT NUMERICAL SIMULATION THAT DISCRETELY CONSERVES MASS, MOMENTUM, AND KINETIC ENERGY

pages 365-370
DOI: 10.1615/TSFP2.1350
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RESUMO

A second-order accurate finite difference discretization of the incompressible Navier-Stokes is presented that discretely conserves mass, momentum, and kinetic energy (in the inviscid limit) in space and time. The method is thus completely free of numerical dissipation and potentially well suited for the direct numerical simulation (DNS) or large-eddy simulation (LES) of turbulent flow. The method uses a staggered arrangement of velocity and pressure on a structured Cartesian grid, and retains its discrete conservation properties for both uniform and non-uniform grid spacing. The predicted conservation properties are confirmed by inviscid simulations on both uniform and non-uniform grids. The suitability of the method for DNS is demonstrated by repeating the turbulent channel flow simulations of Choi and Moin (1994), where the effect of computational time step on the computed turbulence was investigated. Using the present fully-conservative scheme, turbulent flow solutions were achieved for all computational time steps investigated (Δt+ = Δtu2τ = 0.4, 0.8, 1.6, and 3.2). Little variation in statistical turbulence quantities was observed up to Δt+ = 1.6. The present results differ significantly from those reported by Choi and Moin, who observed significant discrepancies in the turbulence statistics above Δt+ = 0.4, and the complete re-laminarization of the flow at and above Δt+ = 1.6.

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