Linear stability analysis of compressible flows using a conservative-variable formulation

High-speed compressible flows are often characterized by the presence of strong gradients that take the form of compression and expansion waves. For these configurations, a well-established practice in CFD consists in solving the governing equations in conservation form. This enables the numerical discretization to act on the conservative variables and the associated flux vectors, thus introducing advantageous wave-capturing capabilities in the solution.

Up to present, the stability analysis of high-speed flows has been almost exclusively performed using primitive-variable formulations, even though the base-flow solutions on which they are deployed usually come from conservative solvers.

By employing a linearization of the Navier-Stokes equations expressed in conservative variables, linear stability analyses of supersonic jet flows and high-speed boundary layers are performed. The resulting spectra and the amplitude functions of different relevant stability mechanisms are described in terms of conservative variables, and are compared against identical analyses based on primitive variables. In addition, non-modal analyses are carried out using both primitive and conservative formulations, and relevant differences between them are discussed.