On the Accuracy of Symmetry-Preserving Discretization

Abstract

We propose to perform turbulent flow simulations in such a 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 × 64 × 32 grid suffices to perform an accurate direct numerical simulation.