Optimal Control of Continuous and Discontinuous Flow

• Other Authors: Homescu, Cristian A. (authoraut)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Mathematics
• Online Access: http://purl.flvc.org/fsu/fd/FSU_migr_etd-4522

Numerical and theoretical aspects of solving optimal control problems for a continuous flow (suppression of the Karman vortex street for a flow around a cylinder) and for a discontinuous flow (changing the location of discontinuities for the shock-tube problem) are considered. The minimization algorithms require the gradient (or a sub-gradient) for the smooth (respectively non smooth) cost functional. The numerical value of the gradient (respectively a sub gradient) is obtained using the ad-joint method. The optimal solutions are verified using their physical interpretation. A very convincing argument for the validity of the numerical optimal solutions is obtained comparing the values corresponding to observed physical phenomena to the above mentioned numerical optimal controls. Sensitivity analysis of a discontinuous flow, namely for t he shock-tube problem of gas dynamics, was also studied. Better results are obtained compared to the available literature, due to the use of adaptive mesh refinement. === A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. === Summer Semester, 2002. === July 15, 2002. === Mathematics, Algorithms, Shock-tube, Gas Dynamics, Adpative Mesh Refinment === Includes bibliographical references. === I. M. Navon, Professor Directing Thesis; R. Pfeffer, Outside Committee Member; M. Y. Hussaini, Committee Member; G. Erlebacher, Committee Member; S. Blumsack, Committee Member.