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Conservative time integrators of arbitrary order for skew-symmetric finite-difference discretizations of compressible flow
Citation key BrouwerReissSesterhenn2014b
Author Jens Brouwer and Julius Reiss and Jörn Sesterhenn
Pages 1 - 12
Year 2014
ISSN 0045-7930
DOI http://dx.doi.org/10.1016/j.compfluid.2014.04.019
Journal Computers & Fluids
Volume 100
Abstract Abstract 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.
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