Section: New Results

Sensitivity equation method for hyperbolic systems

Participants : Régis Duvigneau, Camilla Fiorini [UVST] , Christophe Chalons [UVST] .

While the sensitivity equation method is a common approach for parabolic systems, its use for hyperbolic ones is still tedious, because of the generation of discontinuities in the state solution, yielding Dirac distributions in the sensitivity solution.

To overcome this difficulty, we investigate a modified sensitivity equation, that includes an additional source term when the state solution exhibits discontinuities, to avoid the generation of delta-peaks in the sensitivity solution. We consider as example the one-dimensional barotropic Euler equations. Different approaches are tested to integrate the additional source term: a Roe solver, a Godunov method and a moving cells approach. This study is achieved in collaboration with C. Chalons from University of Versailles, in the context of C. FIorini's PhD work.