High-order relaxation approaches for adjoint-based optimal control problems governed by nonlinear hyperbolic systems of conservation laws

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Authors

Yohana, Elimboto M.
Banda, M.K. (Mapundi)

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Publisher

De Gruyter

Abstract

A computational investigation of optimal control problems which are constrained by hyperbolic systems of conservation laws is presented. The general framework is to employ the adjoint-based optimization to minimize the cost functional of matching-type between the optimal and the target solution. Extension of the numerical schemes to second-order accuracy for systems for the forward and backward problem are applied. In addition a comparative study of two relaxation approaches as solvers for hyperbolic systems is undertaken. In particular optimal control of the 1-D Riemann problem of Euler equations of gas dynamics is studied. The initial values are used as control parameters. The numerical ow obtained by optimal initial conditions matches accurately with observations.

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Keywords

Conservation laws, Relaxation schemes, Adjoint method, Optimal control, Euler equations, Discrete velocity kinetic systems

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Citation

Yohana, EM & Banda, MK 2016, 'High-order relaxation approaches for adjoint-based optimal control problems governed by nonlinear hyperbolic systems of conservation laws', Journal of Numerical Mathematics, vol. 24, no. 1, pp. 45-71.