Poster Session

Outflow Boundary Condition Leading to Minimal Energy Dissipation for an Incompressible Flow

Michal Bathory
Charles University
Czech Rep
A method for determining the boundary condition on artificial boundaries is presented. This method is formulated as an optimization problem for the energy dissipation. We show that this functional attains its minimum on the set of solutions to the stationary Stokes (Navier-Stokes) system with partially unspecified boundary condition. Thus, this method gives rise to a physically reasonable implicit boundary condition which ensures the existence of a solution to the system. In particular, for the Stokes system, this implicit condition implies certain modification of the ``do-nothing`` boundary condition. For the Navier-Stokes system, we foreshadow the ``correct`` explicit boundary condition.