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One‐dimensional turbulence (ODT) based models are able to generate good results for canonical flow problems compared to Direct Numerical Simulations. ODT has been successfully implemented as a sub‐grid scale model for LES problems (ODTLES) delivering promising results. However, due to the computational cost of the ODT model in this scope, there is a need for an even faster model for real world parameter regimes. The Hierarchical Parcel Swapping (HiPS) algorithm used in combination with the ODT model to simulate a channel flow recently provided results with an acceptable quality in a fraction of the time of an ODT simulation. HiPS uses a binary tree to define the fluid domain, and stochastic eddy events are sampled in this tree. A local instantaneous and complete mixing of the cells is performed when an eddy event happens at the Kolmogorov scale. The biggest limitation of this model is that the viscosity of the solution is implicitly defined by the number of cells in a mesh. Further development of HiPS is planned in order to create a computationally cheaper alternative for the ODT model to be used in ODTLES flow simulations. [ABSTRACT FROM AUTHOR]

Hybrid systems combine continuous‐time and discrete‐time dynamics. They emerge in mechanical systems, inter alia, when collisions are modelled by impulse‐like contact forces. During collisions of two or more bodies, the positions of the latter evolve continuously, but their velocities experience jumps. On the one hand, this non‐smoothness significantly complicates the optimal control problem; on the other, it opens up opportunities for new numerical methods. This contribution uses a nested optimization in order to control the swinging up of a hybrid pendulum‐on‐cart‐system. Both, pendulum and cart, move in finite ranges which are bounded by limiters (elastic collisions). The outer layer optimizes the occurrence and the momenta of the collisions, while the inner layer optimizes the smooth motions from start to collision, from collision to collision, and finally to the terminal state. The discretization and the optimal control of continuous‐time dynamics are based on the Discrete‐Mechanics‐and‐Optimal‐Control (DMOC) approach. [ABSTRACT FROM AUTHOR]