A hybrid adjoint approach for systems of arbitrarily complex partial differential equations

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The adjoint method was first developed for fluid dynamics and aerospace applications in the 1970s and 1980s, and has since been applied to an increasingly varied set of problems. Adjoint-based techniques can provide the sensitivity of an objective function to any number of parameters of a simulation inexpensively at roughly the cost of a single additional flow calculation. This information can be used to perform sensitivity analyses, aerodynamic shape optimization and to estimate the error in the objective function due to numerical discretization. Existing approaches to derive adjoint formalisms involve the so-called discrete and continuous methods, which differ in the order of performing the discretization and linearization steps. In this work, an alternative hybrid adjoint approach is proposed with the aim of combining the relative advantages of the continuous and discrete methods, and thus making it easier to apply the adjoint approach to complex problems. The adjoint method can, in general, be derived via a Lagrange multiplier approach, where the governing equations of the primal problem are enforced in the objective function through the adjoint variables. The new hybrid approach developed in this dissertation enforces the flow conservation equations in a continuous manner and additional models, such as those handling turbulence or combustion, discretely. This hybrid approach has been developed with application to both quasi-one-dimensional Euler flow with a simple combustion model and Reynolds-Averaged Navier-Stokes flow with a general turbulence model.


Type of resource text
Form electronic; electronic resource; remote
Extent 1 online resource.
Publication date 2013
Issuance monographic
Language English


Associated with Taylor, Thomas William Richard
Associated with Stanford University, Department of Aeronautics and Astronautics.
Primary advisor Alonso, Juan José, 1968-
Primary advisor Palacios, Francisco, (Research associate)
Thesis advisor Alonso, Juan José, 1968-
Thesis advisor Palacios, Francisco, (Research associate)
Thesis advisor Duraisamy, Karthikeyan
Thesis advisor Iaccarino, Gianluca
Thesis advisor Jameson, Antony, 1934-
Advisor Duraisamy, Karthikeyan
Advisor Iaccarino, Gianluca
Advisor Jameson, Antony, 1934-


Genre Theses

Bibliographic information

Statement of responsibility Thomas William Richard Taylor.
Note Submitted to the Department of Aeronautics and Astronautics.
Thesis Thesis (Ph.D.)--Stanford University, 2013.
Location electronic resource

Access conditions

© 2013 by Thomas William Richard Taylor
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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