On the spectral properties of shock-capturing schemes

By Sergio Pirozzoli. Journal of Computational Physics, 2006

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Optimized sixth‐order monotonicity‐preserving scheme by nonlinear spectral analysis (2013, methodology): “In Pirozzoli’s method, a onedimensional linear convection equation is solved numerically and small time-advanced, and then discrete Fourier transform (DFT) is used for the spectral analysis.”
A family of high-order targeted ENO schemes for compressible-fluid simulations (2016, methodology): “Following Pirozzoli’s ADR analysis [16], Hu et al.”
Numerical Methods for High-Speed Flows (2011, background): “For a discussion of the impact of nonlinearities on the behavior of shock-capturing schemes in Fourier space see Pirozzoli (2006).”
A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations (2009, methodology): “In this case, in order to assess the quality of the solutions, in particular in aeroacoustic studies, there is an urgent need of analysing the spectral properties of the shock-capturing schemes in the Fourier space [25], and of checking their accuracy by solving standard CAA test cases [26,27].”
A new smoothness indicator for third‐order WENO scheme (2016, methodology): “The hybrid methods, as a popular choice, have also been applied to quite a bit of work with respect to simulations of compressible turbulence, the relevant topics can be found in the comprehensive review of Pirozzoli [12].”