Symmetry-Preserving Discretization of Turbulent Channel Flow

摘要

We propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the underlying differential operators, i.e. the convective operator is represented by a skew-symmetric matrix and the diffusive operator is approximated by a symmetric, positive-definite matrix. Such a symmetry-preserving discretization of the Navier-Stokes equations is stable on any grid, and conserves the total mass, momentum and kinetic energy (when the physical dissipation is turned off). Its accuracy is tested for a turbulent channel flow at Re=5,600 (based on the channel width and the mean bulk velocity) by comparing the results to those of physical experiments and previous numerical studies. This comparison shows that with a fourth-order, symmetry-preserving method a 64 x 64 x 32 grid suffices to perform an accurate direct numerical simulation.