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

作者：Yohana Elimboto M; Banda Mapundi K^*

来源：Journal of Numerical Mathematics, 2016, 24(1): 45-71.

DOI：10.1515/jnma-2013-1002

• conservation laws
• relaxation schemes
• adjoint method
• optimal control
• Euler equations
• discrete velocity kinetic systems

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 flow obtained by optimal initial conditions matches accurately with observations.

• 出版日期2016-3