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A conservative, skew-symmetric Finite Difference Scheme for the compressible Navier–Stokes Equations
Citation key ReissSesterhenn2014
Author Julius Reiss and Jörn Sesterhenn
Pages 208 - 219
Year 2014
ISSN 0045-7930
DOI http://dx.doi.org/10.1016/j.compfluid.2014.06.004
Journal Computers & Fluids
Volume 101
Note see also [arXiv:1308.6672]
Abstract Abstract We present a fully conservative, skew-symmetric finite difference scheme on transformed grids. The skew-symmetry preserves the kinetic energy by first principles, simultaneously avoiding a central instability mechanism and numerical damping. In contrast to other skew-symmetric schemes no special averaging procedures are needed. Instead, the scheme builds purely on point-wise operations and derivatives. Any explicit and central derivative can be used, permitting high order and great freedom to optimize the scheme otherwise. This also allows the simple adaption of existing finite difference schemes to improve their stability and damping properties. Numerical examples covering acoustic phenomena and shocks are presented.
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