“…It is a challenge in that the numerical scheme must: (i) handle shock waves, (ii) resolve acoustic waves with low dispersion and dissipation errors, (iii) resolve the instability waves in the jet shear layer and their interaction with the core shock-cell structure, and (iv) have an effective non-reflecting boundary condition. Successful direct computation of screech for circular jets have been carried out by Shen and Tam [10,12] using the Dispersion Relation Preserving, or DRP, scheme and by the present authors [13][14][15][16] using a NavierStokes solver based on the space-time conservation element and solution element, or CE/SE, method [17,18]. In their 3-D computation, Shen and Tam [12] adopted a spectral method in the azimuthal direction and by using only a limited number of spectral functions achieved substantial savings of computer memory and CPU time, without deterioration of accuracy.…”