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@incollection{zahr2018flapopt,
abstract = {A globally high-order numerical discretization of time-dependent conservation laws on deforming domains, and the corresponding fully discrete adjoint method, is reviewed and applied to determine energetically optimal flapping wing motions subject to aerodynamic constraints using a reduced space PDE-constrained optimization framework. The conservation law on a deforming domain is transformed to one on a fixed domain and discretized in space using a high- order discontinuous Galerkin method. An efficient, high-order temporal discretization is achieved using diagonally implicit Runge-Kutta schemes. Quantities of interest, such as the total energy required to complete a flapping cycle and the integrated forces produced on the wing, are discretized in a solver-consistent way, that is, via the same spatio- temporal discretization used for the conservation law. The fully discrete adjoint method is used to compute discretely consistent gradients of the quantities of interest and passed to a black-box, gradient-based nonlinear optimization solver. This framework successfully determines an energetically optimal flapping trajectory such that the net thrust of the wing is zero to within 9 digits after only 12 optimization iterations.},
author = {Zahr, Matthew J. and Persson, Per-Olof},
booktitle = {Frontiers in {PDE}-Constrained Optimization},
contribution = {conceptualization, formal analysis, investigation, writing - original (MJZ); methodology, software (MJZ, PP); resources, writing - edit/review (PP)},
corauthor = {Zahr, Matthew J.},
date-added = {2016-12-06 07:15:11 +0000},
date-modified = {2020-12-31 15:06:30 -0500},
order = {1},
paper = {content/bookch/zahr2017flapopt.pdf},
project = {dgopt},
publisher = {Springer},
title = {Energetically optimal flapping wing motions via adjoint-based optimization and high-order discretizations},
year = {2018}
}
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