Sparse Techniques in Global Flow Instability with Application to Compressible Leading-Edge Flow

Abstract

Investigation of linear instability mechanisms is essential for understanding the process of transition from laminar to turbulent flow. Many studies over several decades have reported results in simple one-dimensional steady laminar basic flows, such as the boundary and shear layers. However, most flows of practical engineering significance remain unexplored. The main reason is that the geometry and underlying basic state in most applications depend on an inhomogeneous manner on more than one spatial direction,
\nwhich does not permit use of simplified equations. The consideration of two or three inhomogeneous directions in the stability problem formulation results in formidable computational costs for completing parametric studies, which are, on the other hand, mandatory from a physical point of view.