Analysis of Transient Behavior in Linear Differential Algebraic Equations
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چکیده
The linearized Navier-Stokes equations form a type of system called a differential algebraic equation (DAE). These equations impose both algebraic and differential constraints on the solution, and present significant challenges to solving. This paper discusses a method for solving DAEs by the Schur factorization to avoid some of the obstacles that are typically present. We also investigate the transient behavior of the solution using results from pseudospectral theory, which will help us understand whether the solution to the linearized Navier-Stokes system will become turbulent if its steady state is disturbed. If a flow does indeed grow substantially in energy, then we must be cautious about using the linearized model. Thus, having information about transient behavior is quite instructive.
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