Comparative Analysis of Three Different Eigenvalue Solvers for Linear Stability Analysis
Rômulo Bessi Freitas1; Leonardo Santos de Brito Alves1
1 Universidade Federal Fluminense - UFF
doi:10.20906/CPS/COB-2015-2037
Resumo
There are several engineering problems, mainly in aerodynamic applications, where it is crucial to understand the flow transition from laminar to turbulent. For example, wing design in order to reduce drag on commercial and military aircraft,intensification of the fuel/oxidant in combustion chambers of rocket engines and so on. For the best part of the last century, instability analysis was performed using the classical theory of normal modes and it still has important relevance for several problems. Today in local analysis, disturbances are assumed homogeneous in two out of the three spatial directions and, then, the eigevalue problem for incompressible flows reduces to the Orr-Sommerfeld equation. Shooting method are one of the traditional ways to solve this problem. However, it can be quite hard to determine suitable initial guess and locate all the important modes. An alternative approach is known as the matrix forming method, which transforms the Linearized Navier-Stokes Equations (LNSE) into a generalized eigenvalue problem that provides all available. Recently, a novel approach known as time stepper method marches the LNSE in time until the leading eigemode dominates the asymptotic temporal behaviour. The present paper provides an instability analysis for mixing layers using all three methods in order to compare them and evaluate their potential advantages and disdvantages when simulating instability problems for incompressible flows.
Palavras-chave: Stability analysis; Shooting method; Matrix forming; Time steppers; stability of mixing layer