Optimal control of coupled multiphysics problems: Guidelines for real‐life applications demonstrated for a complex fuel cell model

Abstract

AbstractIn practice one often is confronted with the simulation and optimization of dynamical processes of multiphysics systems depending on time and space. This paper shall serve as a guidebook for practioneers who wants to proceed from simulation to optimization. We are specially concerned in this paper with optimal control problems involving partial differential equations. After providing an insight into the theory of optimal control problems with partial differential equations, the focus of the paper lies on their numerical treatment to obtain approximate optimal solutions, or more precisely approximate candidate optimal solutions. The two basic approaches, first optimize then discretize (FOTD) and first discretize then optimize (FDTO) are first described in an abstract setting and then evaluated by means of the fuel cell example of this paper which can serve as a prototype problem for multiphysics processes. The example describes the dynamical behaviour inside a certain type of high temperature fuel cell where gas flows, heat distribution, and potential fields as well as chemical reactions are modelled by hyperbolic and parabolic partial differential as well as ordinary differential algebraic equations. The underlying problem is an optimal control problem where up to 28 instationary partial differential algebraic equations in one, respectively two spatial dimensions are involved. In the conclusion pros and cons of the aforementioned approaches are discussed. Hereby, not only the numerical efficiency but also the investigation of human resources are balanced against each other (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)