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

Jan Nordström
Division of Scientific Computing
Department of Information Technology
Uppsala University
and
Swedish Defence Research Agency FOI
Stockholm

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.