Numerical Spectral Analysis of Temporal Stability of Laminar Duct Flows with Constant Cross Sections

Problems related to the temporal stability of laminar viscous incompressible flows in ducts with a constant cross section are formulated, justified, and numerically solved. For the systems of ordinary differential and algebraic equations obtained by a spatial approximation, a new dimension reduction technique is proposed and substantiated. The solutions to the reduced systems are decomposed over subspaces of modes, which considerably improves the computational stability of the method and reduces the computational costs as compared with the usual decompositions over individual modes. The optimal disturbance problem is considered as an example. Numerical results for Poiseuille flows in a square duct are presented and discussed.