Michael Herty

Optimal control problems for the radiative transfer equation and for approximate models are considered. Following the approach first discretize, then optimize, the discrete SP_N approximations are for the first time derived exactly and used for the study of optimal control based on reduced order models. Moreover, combining asymptotic analysis and the adjoint calculus yields diffusion‐type approximations for the adjoint radiative transport equation in the spirit of the approach first optimize, then discretize.

We introduce a model for gas flow in pipeline networks based on the isothermal Euler equations. We model the intersection of multiple pipes by posing an additional assumption on the pressure at the interface. We give a method to obtain solutions to the gas network problem and present numerical results for sample networks.

We investigate coupling conditions for gas transport in networks where the governing equations are the isothermal Euler equations. We discuss intersections of pipes by considering solutions to Riemann problems. We introduce additional assumptions to obtain a solution near the intersection and we present numerical results for sample networks.

We consider coupling conditions for the “Aw–Rascle” (AR) traffic flow model at an arbitrary road intersection. In contrast with coupling conditions previously introduced in [10] and [7], all the moments of the AR system are conserved and the total flux at the junction is maximized. This nonlinear optimization problem is solved completely. We show how the two simple cases of merging and diverging junctions can be extended to more complex junctions, like roundabouts. Finally, we present some numerical results.