An energy-stable generalized-α method for the Swift-Hohenberg equation

An energy-stable generalized-α method for the Swift-Hohenberg equation

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-a method and provides control over dissipation via the...

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Bibliographic Details
Main Authors: Sarmiento, A., Espath, L., Vignal, P., Dalcin, L., Parsani, M., Calo, Victor
Format: Journal Article
Published: Elsevier 2017
Online Access:http://hdl.handle.net/20.500.11937/63144
Description
Summary: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-a 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.

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