Sensitivity analysis for PDE systems consists in estimating the derivatives of the solution fields with respect to problem parameters, that can affect for instance the geometry, the boundary conditions or model coefficients. Sensitivity solutions can be applied to differents purposes, such as optimization, uncertainty quantification or fast estimation of neighbor solutions. This work is carried out in the context of the Continuous Sensitivity Equation (CSE) method.

Research axes

  • Sensitivity analysis for unsteady compressible flows: We investigate the application of the CSE method to Navier-Stokes equations, for time-dependent problems like active flow control. In particular, we aim at estimating high-order solution derivatives.

  • Sensitivity analysis for discontinuous state solutions: When the solution exhibits discontinuities, like shock waves, sensitivity analysis becomes tedious, due to the emergence of Dirac functions in the sensitivity. We investigate how to alleviate this difficulty by modifying locally the CSE.

Some related papers

  • Sensitivity analysis for the Euler equations in Lagrangian coordinates, C. Chalons, R. Duvigneau, C. Fiorini, Finite-Volumes for Complex Applications, Lille, June 2017

  • Parametric optimization of pulsating jets in unsteady flow by Multiple-Gradient Descent Algorithm, J.-A. Désidéri & R. Duvigneau, Numerical Methods for Differential Equations, Optimization, and Technological Problems, Springer, 2017.

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Velocity (top) and sensitivity (down) fields for a plate equipped with an oscillatory jet.