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High-Order Taylor Expansions for Compressible Flows

Régis Duvigneau 1
1 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Sensitivity analysis for systems governed by partial differential equations is now commonly used by engineers to assess performance modification due to parameter changes. A typical illustration concerns shape optimization procedures based on the adjoint method, used in aeronautics to improve aerodynamic or structural performance of aircrafts. However, these approaches are usually limited to first-order derivatives and steady PDE systems, due to the complexity to extend the adjoint method to higher-order derivatives and the associated reverse time integration. Alternatively, this work investigates the use of the direct differentiation approach (continuous sensitivity equation method) to estimate high-order derivatives for unsteady flows. We show how this method can be efficiently implemented in existing solvers, in the perspective of providing a Taylor expansion of the PDE solution with respect to control parameters. Applications to optimization and uncertainty estimation are finally considered.
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https://hal.inria.fr/hal-01589254
Contributor : Régis Duvigneau <>
Submitted on : Monday, September 18, 2017 - 1:47:00 PM
Last modification on : Thursday, May 20, 2021 - 9:12:01 AM

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  • HAL Id : hal-01589254, version 1

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Régis Duvigneau. High-Order Taylor Expansions for Compressible Flows. SIAM Optimization, May 2017, Vancouver, Canada. ⟨hal-01589254⟩

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