Abstract of the paper ``Normalization constraint for variational bounds on
fluid permeability'' with Graeme W. Milton
A careful reexamination of the formulation of Prager's original variational
principle for viscous flow through porous media has uncovered a subtle error
in the normalization constraint on the trial functions.
Although a certain surface integral of the true pressure field over the
internal surface area always vanishes for isotropic materials, the
corresponding surface integral for a given trial pressure field does not
necessarily vanish but has nevertheless been previously neglected in the
normalization. When this error is corrected, the form of the variational
estimate is actually simpler than before and furthermore the resulting bounds
have been shown to improve when the constant trial functions are used in
either the two-point or three-point bounds.
Electronic copies of this paper are not available.