Semi-Implicit Runge-Kutta Schemes: Development and Application to Compressible Channel Flow

time stepconstraintdueto thefine meshnear thewall.The explicitsubschemeis asix-stage fourth-order low-storage Runge–Kutta scheme. Based on analysis in Fourier space and results obtained for propagation test cases, the semiimplicitschemesareshowntobeoforder3and,forwavesdiscretizedbyanumberofpointsperperiodbetween4and 16,tobeasaccurateas,ormoreaccuratethan,thestandardexplicitfourth-orderRunge–Kuttaalgorithmintermsof dissipationanddispersion.Thelarge-eddysimulationofacompressibleturbulentchannelflowatafrictionReynolds numberof360andaMachnumberof0.1isthencarriedoutwithoneoftheproposedalgorithms.Thecomputational time is reduced by a factor 1.33 with respect to a large-eddy simulation using the explicit subscheme in all directions. Wall-pressure and velocity spectra from the large-eddy simulation are presented to give insights into the flow turbulent structures. In particular, wave number–frequency spectra are calculated. Acoustic components appear to be identified in these spectra.

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