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Many partial differential equations consist of slow and fast scales. Often, the right hand side of semidiscretized PDEs can be split additively in corresponding fast and slow parts. Many methods utilise the additive splitting of these equations, like generalized additive Runge‐Kutta (GARK) methods or multirate infinitesimal step methods. The latter one treat the slow part with macro step sizes, whereas...
In high‐pressure die casting, the quality of the produced cast parts highly depends on the die quality. One die component are temperature control channels. The state‐of‐the art approach for the temperature control channels are boreholes drilled from the sides into the die that are afterwards formed into a closed flow channel by inserting plugs.
Since additive manufacturing methods are available to...
This paper shows how an electrical distribution network can be modeled as constraints of a continuous nonlinear optimization problem. The objective is to minimize the deviation from a given nominal voltage. We explain how this setup can be used to optimize wire diameters within the network. Thus we find the optimal expansion of the network by identifying wires which should be enforced. The results...
Two Markov chain Monte Carlo simulation methods for reliability estimation, subset simulation and the moving particles algorithm, are compared based on theoretical arguments and test cases. The differences in the efficiency between both algorithms are rather small. They seem to be well suited for off‐the‐shelf reliability estimations, but with a different setting for the most important parameters...
In future the model quality will have an increasing priority in the industrial context and suitable techniques and methods to quantify them have to be developed. In this paper we want to focus on the challenge of selecting the most informative measurement data for a time‐dependent simulation model to infer parameter distributions. Sobol indices are used to give a estimate about the global sensitivity...
Many modern high‐performance materials have inherent anisotropic elastic properties and its local material orientation can be considered to be an additional design variable for the topology optimization [1–3]. We extend our previous model for topology optimization with variational controlled growth [4–6] for linear elastic anisotropic materials, for which the material orientation is introduced as...
We consider linear dynamical systems including random variables for an uncertainty quantification. A quantity of interest is expanded into a series with orthogonal basis polynomials. We investigate a Hankel‐type norm of a truncated series. An approximation of this norm can be obtained by a quadrature formula, which implies a larger weakly coupled system. We present results of numerical computations...
The results of theoretical and experimental investigation into resonance phenomena accompanying guided wave propagation in a metallic plate with a finite regular system of rectangular deep notches are presented. While the expected intensification of wave blocking by a system of notches comparing to the case of a single defect is confirmed, the resonance transmission at the predicted frequencies within...
Lithium‐ion batteries are composed of several single cells, each consisting of conductive, impermeable electrodes made of aluminum and copper. Both are coated with a thin, porous layer on both sides (collectors) and a thin, non‐conductive and permeable layer is separating them. As the layers are stacked, the liquid enters the battery at all front edges, while the gas is trapped inside. To estimate...
Sloshing in a fuel tank of a commercial vehicle, which is subdivided by a perforated plate as baffle, is investigated to predict occuring forces. Using linear potential theory and a two‐dimensional modal description, the eigenmodes and eigenfrequencies are determined for the baffled tank and compared to experimental results. Damping due to viscous boundary layers and the pressure drop at the baffle...
A time‐domain approach for the simulation of elastic waves in heterogeneous soil domains is presented. It is based on modelling both near and far field by the scaled boundary finite element method (SBFEM). The SBFEM facilitates the use of a structured mesh in the near field region without the need to circumvent hanging nodes. The quadtree mesh is obtained automatically from image data. Radiation damping...
Particle trajectories in an incompressible cavity flow are investigated experimentally. The flow is driven by two facing walls moving with same speed in opposite directions. When the flow is steady and three‐dimensional, finite‐size and neutrally‐buoyant particles are rapidly attracted to periodic orbits. Three‐dimensional particle tracking is used to reconstruct single particle trajectories. Experimental...
The Stochastic Field Method was introduced in the field of combustion and represents a Eulerian Monte‐Carlo technique. It was first transfered to the field of multiphase flow in [1] facing a problem in nuclear technology. Within this work it is applied to cavitating flows in the automotive sector. Both phases, the continuous and the dispersed phase, are observed using a Eulerian perspective which...
Microbeams are building blocks for many microstructures as well as microelectromechanical systems (MEMS) and cannot accurately be modelled by classical continuum theories due to size effects based on their micro‐scale. These size effects can be taken into account by the so‐called higher order continuum theories. Modified Strain Gradient Theory (MSGT) and Modified Couple Stress Theory (MCST) are two...
The phase retrieval problem consists in the recovery of a complex‐valued signal from the magnitudes of its Fourier transform. Restricting ourselves to the case of sparse structured signals f, which can be represented as a linear combination of N arbitrary translations of a given generator function, we show that almost all f can be recovered from 𝒪 (N2) intensity measurements |ℱ[f](ω)| up to trivial...
In this paper, we consider a class of controlled population balance equations describing granulation processes in chemical engineering. Such a control system admits an equilibrium which is not asymptotically stable in general. In order to stabilize this equilibrium, we consider the perturbed system and introduce a Lyapunov functional candidate as a weighted L2‐norm. It is shown that the weight function...
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