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.
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.