Conservative time integrators of arbitrary order for skew-symmetric finite-difference discretizations of compressible flow

Skew-symmetric discretizations of the Navier-Stokes equations avoid the introduction of artificial numerical damping by first principles and are thus attractive for the simulation of turbulence and flow induced sound. For direct numerical simulations a high discretization order in space and time is essential to obtain high quality results at affordable cost. While skew-symmetric and fully conservative schemes of high spatial discretization order are available, the time integrators respecting skew-symmetry and conservation are of second order only. We present a class of time integrators for skew-symmetrical schemes for compressible flow, which allow an arbitrary order of accuracy. We also show that these schemes are discretely norm-conserving. Test cases for isotropic turbulence are performed. A comparison with standard spatial and temporal discretization completes our survey. (C) 2014 Elsevier Ltd. All rights reserved.