Dynamic Boundary Conditions In Cfd.

Abstract

The number and type of boundary conditions to be used in the numerical modeling
of fluid mechanics problems is normally chosen according to a simplified analysis of the characteristics,
and also from the experience of the modeler. The problem is harder at input/output
boundaries which are, in most cases, artificial boundaries, so that a bad decision about the
boundary conditions to be imposed may affect the precision and stability of the whole computation.
For inviscid flows, the analysis of the sense of propagation in the normal direction to
the boundaries gives the number of conditions to be imposed and, in addition, the conditions
that are “absorbing” for the waves impinging normal to the boundary. In practice, it amounts
to counting the number of positive and negative eigenvalues of the advective flux Jacobian projected
onto the normal. The problem is still harder when the number of incoming characteristics
varies during the computation, and to correctly treat these cases poses both mathematical and
practical problems. One example considered here is compressible flow where the flow regime
at a certain part of an inlet/outlet boundary can change from subsonic to supersonic and the
flow can revert. In this work the technique for dynamically imposing the correct number of
boundary conditions along the computation, using Lagrange multipliers and penalization is
discussed, and several numerical examples are presented.