SENSITIVITY CALCULATIONS FOR CONSERVATION LAWS WITH APPLICATION TO
DISCONTINUOUS FLUID FLOWS
by
Justin Ronald Appel
PhD Dissertation submitted to the Faculty of the Virginia Tech
in partial fulfillment of the requirements or
the degree of
Doctor of Philosophy
in
Mathematics
Approved
Max D. Gunzburger, Chair
John A. Burns
Eugene M. Cliff
Terry L. Herdman
Janet S. Peterson
March 14, 1997
Blacksburg, Virginia
Flow sensitivities are the derivatives of the variables that describe
the fluid flow with respect to the parameters that determine the fluid
flow. Sensitivities are of interest in their own right and are also of
use in flow optimization,
control and design and in the calculation of perturbed flows.
Problems arise in
all sensitivity calculation methods in the presence of discontinuities
and other complexities such as shock waves, contact discontinuities
and rarefaction waves that commonly occur in super and hypersonic inviscid,
compressible fluid flows. Flow sensitivities are calculated using finite
difference quotients, automatic differentiation and the sensitivity
equation method for a variety of numerical methods. Explanations
for the inaccuracies arising in the numerical approximations
and implications these inaccuracies have on different
applications are discussed. Possible corrections for the inaccuracies
are outlined.
