Scholarly Communications Project


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


Abstract

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.

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