| Abstract | Weighted essentially non-oscillatory (WENO) methods have been developed to simul-taneously provide robust shock-capturing in compressible fluid flow and avoid excessive
damping of fine-scale flow features such as turbulence. Under certain conditions in com-
pressible turbulence, however, numerical dissipation remains unacceptably high even after
optimization of the linear component that dominates in smooth regions. We demonstrate
that a significant nonlinear source of dissipation error is due to a WENO implementa-
tion defect that we call the “synchronization deficiency,” and we develop and evaluate a
preliminary technique to mitigate its effects. Direct numerical simulations (DNS) include
one-dimensional test cases and three-dimensional compressible isotropic turbulence. Al-
though we find the current formulation of our mitigation technique to be quite successful
for the one-dimensional problems, its efficacy is more modest in the turbulence simulations,
and its cost-to-benefit ratio is uncomfortably high. We believe, however, that with further
work it will be possible to alleviate these drawbacks.
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