Parametric Optimization of Pulsating Jets in Unsteady Flow by Multiple-Gradient Descent Algorithm (MGDA)

  • Jean-Antoine DésidériEmail author
  • Régis Duvigneau
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 47)


Two numerical methodologies are combined to optimize six design characteristics of a system of pulsating jets acting on a laminar boundary layer governed by the compressible Navier-Stokes equations in a time-periodic regime. The flow is simulated by second-order in time and space finite-volumes, and the simulation provides the drag as a function of time. Simultaneously, the sensitivity equations, obtained by differentiating the governing equations w.r.t. the six parameters are also marched in time, and this provides the six-component parametric gradient of drag. When the periodic regime is reached numerically, one thus disposes of an objective-function, drag, to be minimized, and its parametric gradient, at all times of a period. Second, the parametric optimization is conducted as a multi-point problem by the Multiple-Gradient Descent Algorithm (MGDA) which permits to reduce the objective-function at all times simultaneously, and not simply in the sense of a weighted average.


Active-flow control Time-dependent Navier-Stokes equations Finite-volume schemes Sensitivity equations Multi-objective differentiable optimization Descent methods Robust design 


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.INRIA Acumes TeamSophia-AntipolisFrance

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