On the accuracy of the calculation of transient growth in plane Poiseuille flow

This paper addresses the accuracy of numerical methods to compute the transient energy growth of plane Poiseuille flow. We show that using the Chebyshev collocation method to discretize the linearized governing equations in the wall-normal direction can introduce numerical problems when computing the energy evolution of the flow. We demonstrate that spurious eigenmodes of the discretized linear operator and numerical integration errors are the possible sources of the numerical problems, and we also show that spurious eigenvalues with negative real parts of large magnitude can affect the calculation of energy growth. These difficulties can be avoided by using a spectral Galerkin method where the basis functions satisfy the boundary conditions. Copyright (c) 2014 John Wiley & Sons, Ltd.