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In this article a framework for the generation of a computationally fast surrogate model for district heating networks is presented. An appropriate model is given by in an index-1 hyperbolic, differential algebraic equation quadratic in state, exhibiting several hundred of outputs to be approximated. We show the existence of a global energy matrix which fulfills the Lyapunov inequality ensuring stability of the reduced model. By considering algebraic variables as parameters of the dynamical transport, a time varying (LTV) problem has to be reduced. We present a scheme to efficiently combine linear reductions to a global surrogate model using a greedy strategy in the frequency domain. The numerical effectiveness of the scheme is demonstrated at different, existing, large scale networks.

Modeling and simulation of disease spreading in pedestrian crowds have recently become a topic of increasing relevance. In this paper, we consider the influence of the crowd motion in a complex dynamical environment on the course of infection of the pedestrians. To model the pedestrian dynamics, we consider a kinetic equation for multi-group pedestrian flow based on a social force model coupled with an Eikonal equation. This model is coupled with a non-local SEIS contagion model for disease spread, where besides the description of local contacts, the influence of contact times has also been modeled. Hydrodynamic approximations of the coupled system are derived. Finally, simulations of the hydrodynamic model are carried out using a mesh-free particle method. Different numerical test cases are investigated, including uni- and bi-directional flow in a passage with and without obstacles.

This paper deals with the relation of the dynamic elastic Cosserat rod model and the Kirchhoff beam equations. We show that the Kirchhoff beam without angular inertia is the asymptotic limit of the Cosserat rod, as the slenderness parameter (ratio between rod diameter and length) and the Mach number (ratio between rod velocity and typical speed of sound) approach zero, i.e., low-Mach-number–slenderness limit. The asymptotic framework is exact up to fourth order in the small parameter and reveals a mathematical structure that allows a uniform handling of the transition regime between the models. To investigate this regime numerically, we apply a scheme that is based on a Gauss–Legendre collocation in space and an α-method in time.

We study the optimal control of district heating networks using a reduced order model based on a system theoretic description close to the underlying Euler equations. In the presented scenarios, the central task is to limit the maximal feed-in power occurring as a product of control and state variables. The underlying dynamics of heating networks acting as optimization constraints pose the central computational complexity, prohibiting the determination of an optimal control online. The advection of the injected energy density on the network results in an index-1, quadratic in state differential algebraic equation, challenging to reduce. The suggested reduced model decreases the computation time of the optimization significantly. The effectiveness of the presented approach is demonstrated for an existing, large-scale heating network including changes of flux directions.

In this paper we present simulations of moving rigid bodies immersed in a rarefied gas. The rarefied gas is simulated by solving the Bhatnager-Gross-Krook (BGK) model for the Boltzmann equation. The Newton-Euler equations are solved to simulate the rigid body motion. The force and the torque on the rigid body is computed from the surrounded gas. An explicit Euler scheme is used for the time integration of the Newton-Euler equations. The BGK model is solved by the semi-Lagrangian method suggested by Russo & Filbet [ 22 ]. Due to the motion of the rigid body, the computational domain for the rarefied gas (and the interface between the rigid body and the gas domain) changes with respect to time. To allow a simpler handling of the interface motion we have used a meshfree method for the interpolation procedure in the semi-Lagrangian scheme. We have considered a one way, as well as a two-way coupling of rigid body and gas flow. We use diffuse reflection boundary conditions on the rigid body and also on the boundary of the computational domain. In one space dimension the numerical results are compared with analytical as well as with Direct Simulation Monte Carlo (DSMC) solutions of the Boltzmann equation. In the two-dimensional case results are compared with DSMC simulations for the Boltzmann equation and with results obtained by other researchers. Several test problems and applications illustrate the versatility of the approach.

In this paper we present the comparison of experiments and numerical simulations for bubble cutting by a wire. The air bubble is surrounded by water. In the experimental setup an air bubble is injected on the bottom of a water column. When the bubble rises and contacts the wire, it is separated into two daughter bubbles. The flow is modeled by the incompressible Navier-Stokes equations. A meshfree method is used to simulate the bubble cutting. We have observed that the experimental and numerical results are in very good agreement. Moreover, we have further presented simulation results for liquid with higher viscosity. In this case the numerical results are close to previously published results., Comment: 20 pages, 12 figures. arXiv admin note: text overlap with arXiv:1406.4734