Analytical Solution: Category 4

The propagation of sound waves through non-uniform fluid flows can be described by the linearized Euler equations. However, the linearized Euler equations also support instability wave solutions. For parallel mean flows, these are unstable eigensolutions that, for a jet, are the Kelvin-Helmholtz instability waves. These instability waves can completely overwhelm the acoustic-wave solution. Thus, in order to characterize the properties of the acoustic waves alone, it is important to filter out the unwanted instability waves. The objective of this benchmark problem is to develop a numerical scheme that captures only the acoustic wave solution of the linearized Euler equations.