Stable Robin solid wall boundary conditions for the Navier-Stokes equations

  • Authors:

  • Jens Berg;Jan Nordström

  • Affiliations:

  • Uppsala University, Department of Information Technology, SE-751 05 Uppsala, Sweden;Linköping University, Department of Mathematics, SE-581 83 Linköping, Sweden

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

In this paper we prove stability of Robin solid wall boundary conditions for the compressible Navier-Stokes equations. Applications include the no-slip boundary conditions with prescribed temperature or temperature gradient and the first order slip-flow boundary conditions. The formulation is uniform and the transitions between different boundary conditions are done by a change of parameters. We give different sharp energy estimates depending on the choice of parameters. The discretization is done using finite differences on Summation-By-Parts form with weak boundary conditions using the Simultaneous Approximation Term. We verify convergence by the method of manufactured solutions and show computations of flows ranging from no-slip to almost full slip.