Boundary conditions for a divergence free velocity-pressure formulation of the Navier-Stokes equations

Authors:
Jan Nordström;Ken Mattsson;Charles Swanson
Affiliations:
Department of Information Technology, Scientific Computing, Uppsala University, SE-751 05 Uppsala, Sweden and Department of Aeronautical and Vehicle Engineering, KTH-The Royal Institute of Technol ...;Center for Turbulence Research, Stanford University, Stanford, CA 94305-3035, USA;Computational Aero Sciences Branch, NASA Langley Research Center, Hampton, VI 23681, USA
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

New sets of boundary conditions for the velocity-pressure formulation of the incompressible Navier-Stokes equations are derived. The boundary conditions have the same form on both inflow and outflow boundaries and lead to a divergence free solution. Moreover, the specific form of the boundary condition makes it possible derive a symmetric positive definite equation system for the internal pressure. Numerical experiments support the theoretical conclusions.