Chebyshev-like generalized Shapiro filters for high-accuracy flow computations

This paper presents Chebyshev-like generalized Shapiro (CS) filters with improved spectral-like resolution compared to existing generalized Shapiro filters. These new filters combine the advantages of Shapiro filters, i.e. arbitrary accuracy order, no-dispersion, full damping of 2Δ-waves, and the advantages of Chebyshev filters, i.e. purely dissipative response function with equal ripples satisfying an arbitrary Chebyshev criterion in passband. Thanks to the formalism of generalized Shapiro filters, general formulas are derived for arbitrary accuracy orders and arbitrary Chebyshev criterion. A python script is provided in appendix to compute CS filter coefficients. Computations based on the Euler equations assess the benefit of CS filters compared to the standard Shapiro filters. Since CS filters differ from Shapiro filters only by their coefficients, they can easily and advantageously be implemented in computational solvers already making use of generalized Shapiro filters.