An Auto-Adaptive Multidomain Spectral Technique for Linear Stability Analysis: Application to Viscous Compressible Flows

An auto-adaptive multidomain pseudo-spectral technique is considered in order to solve the linear stability problem of viscous compressible flows. Both the locations of the interfaces and the parameters of the mappings in each subdomain are adapted by minimizing the H ² -norm of the calculated solution. Such method provides automatically—this is the key point—the best polynomial interpolation of the basic state the stability of which is studied. It turns out that the whole procedure is needed to obtain reliable results. The method is first validated against results available in the literature (both viscous incompressible and inviscid compressible Rayleigh–Taylor configurations). The efficiency of the numerical method is illustrated with results on the linear stability of the compressible viscous diffusive Rayleigh–Taylor flow where no analytical or numerical results are available. New results showing the influence of stratification, viscosity, diffusity between species and thermal diffusivity are presented.