Small-scale divergence penalization for incompressible flow problems via time relaxation

Abstract

We study continuous Galerkin finite-element methods for incompressible fluid flow simulation, equipped with the time relaxation of velocity divergence. We show that this (consistent) time relaxation term penalizes small-scale fluctuations in the divergence and present efficient algorithms for its use where the filtering and deconvolution steps are decoupled from the momentum–mass system. Several numerical experiments are provided that demonstrate that more accurate solutions with improved mass conservation are obtained by addition of the time relaxation term to some commonly employed finite-element methods, both for Newtonian and non-Newtonian fluids.

Keywords:

• mass conservation
• time relaxation
• finite-element method
• approximate deconvolution
• Navier–Stokes equations
• Oldroyd-B model

2010 AMS Subject Classifications :

• 35Q30
• 65M12
• 65N30
• 76D05
• 76F65

Acknowledgements

This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, LLNL-JRNL-465054.