Eliminating spurious eigenvalues in the analysis of incompressible fluids and other systems of differential-algebraic equations

摘要: We describe a general framework for avoiding spurious eigenvalues -- unphysical unstable that often occur in hydrodynamic stability problems. In two example problems, we show when system is analyzed numerically using {\em descriptor} notation, are eliminated. Descriptor notation generalized eigenvalue formulation differential-algebraic equations explicitly retains algebraic constraints. propose likely to constraints used analytically reduce the number of independent variables before approximated numerically. contrast, simple and easily generalizable descriptor simultaneously solves differential well-suited analysis these systems.