Abstract
We propose a second-order accurate energy-stable time-integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest resolved frequencies. Our algorithm further extends the generalized-alpha method and provides control over dissipation via the spectral radius. We derive the first and second laws of thermodynamics for the Swift-Hohenberg equation and provide a detailed proof of the unconditional energy stability of our algorithm. Finally, we present numerical results to verify the energy stability and its second-order accuracy in time. (C) 2017 Elsevier B.V. All rights reserved.