Optimal control of flow with discontinuities

Authors:
Chris Homescu;I. M. Navon
Affiliations:
Department of Mathematics and C.S.I.T., Florida State University, Tallahassee, FL;Department of Mathematics and C.S.I.T., Florida State University, Tallahassee, FL
Venue:
Journal of Computational Physics
Year:
2003

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Abstract

Optimal control of the 1-D Riemann problem of Euler equations is studied, with the initial values for pressure and density as control parameters. The least-squares type cost functional employs either distributed observations in time or observations calculated at the end of the assimilation window. Existence of solutions for the optimal control problem is proven. Smooth and nonsmooth optimization methods employ the numerical gradient (respectively, a subgradient) of the cost functional, obtained from the adjoint of the discrete forward model. The numerical flow obtained with the optimal initial conditions obtained from the nonsmooth minimization matches very well with the observations. The algorithm for smooth minimization converges for the shorter time horizon but fails to perform satisfactorily for the longer time horizon, except when the observations corresponding to shocks are detected and removed.