Yohana, Elimboto M.Banda, M.K. (Mapundi)2016-07-272016-03Yohana, 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. 45-71.1570-2820 (print)1659-3953 (online)10.1515/jnma-2013-1002http://hdl.handle.net/2263/56051A 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.en© 2016 Walter de GruyterConservation lawsRelaxation schemesAdjoint methodOptimal controlEuler equationsDiscrete velocity kinetic systemsArticle