Abstract
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 to the direct numerical simulation or large-eddy simulation 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 nonuniform gird spacing. The predicted conservation properties are confirmed by inviscid simulations on both uniform and nonuniform grids. The capability of the method to resolve turbulent flow is demonstrated by repeating the turbulent channel flow simulations of H. Choi and P. Moin (1994, J. Comput. Phys.113, 1), where the effect of computational time step on the computed turbulence was investigated. The present fully conservative scheme achieved turbulent flow solutions over the entire range of computational time steps investigated (Δt+=Δtu2τ/ν=0.4 to 5.0). 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 laminarization of the flow at and above Δt+=1.6.
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