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

摘要

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