Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations

  • Authors:

  • Jan Nordström;Sofia Eriksson;Peter Eliasson

  • Affiliations:

  • Department of Mathematics, Scientific Computing, Linköping University, SE-581 83 Linköping, Sweden;Department of Information Technology, Scientific Computing, Uppsala University, SE-751 05 Uppsala, Sweden;Department of Aeronautics and Systems Integration, FOI, The Swedish Defense Research Agency, SE-164 90 Stockholm, Sweden

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

We study the influence of different implementations of no-slip solid wall boundary conditions on the convergence to steady-state of the Navier-Stokes equations. The various approaches are investigated using the energy method and an eigenvalue analysis. It is shown that the weak implementation is superior and enhances the convergence to steady-state for coarse meshes. It is also demonstrated that all the stable approaches produce the same convergence rate as the mesh size goes to zero. The numerical results obtained by using a fully nonlinear finite volume solver support the theoretical findings from the linear analysis.