Maxwell's Equations in Accelerated Reference Frames and their Application in Computational Electromagnetism

Abstract In many engineering applications the interaction between the electromagnetic field and moving bodies is of great interest. E.g., motional induced eddy currents have to be taken into account correctly for the modelling and simulation of high-speed solenoid actuators. In connection with computational electromagnetism, it seems natural to use a Lagrangian (also called material) description. The unknowns are defined on the mesh, which moves and deforms together with the considered objects. What is the correct form of Maxwell's and the constitutive equations under such circumstances? Since the bodies might undergo accelerated motion, this question cannot in general be answered by the application of Lorentz transforms. Consequently, Maxwell's equations do not necessarily have their usual form in accelerated frames of reference. This was demonstrated in a classical paper by Schiff [1], where it is shown that a significant difference occurs even at "low" velocities, which are small compared to the velocity of light. In contrast, it is convenient to perform the analysis of rotating induction machines from the rotor's point of view. Despite the acceleration, starting from the usual form of Maxwell's equations yields the correct results. How could that be possible? There are only few publications that address the subject from a general point of view and not only for a restricted class of examples, e.g. Moreover, DFs allow separating the topological from the metric part of the theory. Using a noninertial frame induces a metric that is different from the standard Lorentz metric. This metric enters the formulation only through the coordinate expression for the four-dimensional Hodge operator. A localization transform can be introduced, to revert to a (3+1)-dimensional description. This is connected to the concept of a co-moving observer. The result is a relativistically correct Lagrangian form of Maxwell's and the constitutive equations. For "small" accelerations, i.e. if the extension of the system is neglectable compared to the radii of curvature, a concise set of transforms for all the relevant field quantities can be derived. These transforms are well suited for the implementation into numerical field computation codes

Numerical Methods for Flow in Fractured Porous Media

In this work we present the mathematical models for single-phase flow in fractured porous media. An overview of the most common approaches is considered, which includes continuous fracture models and discrete fracture models. For the latter, we discuss strategies that are developed in literature for its numerical solution mainly related to the geometrical relation between the fractures and porous media grids

A monotone multigrid solver for two body contact problems in biomechanics

The purpose of the paper is to apply monotone multigrid methods to static and dynamic biomechanical contact problems. In space, a finite element method involving a mortar discretization of the contact conditions is used. In time, a new contact-stabilized Newmark scheme is presented. Numerical experiments for a two body Hertzian contact problem and a biomechanical application are reported

Modeling and discretization of flow in porous media with thin, full-tensor permeability inclusions

When modeling fluid flow in fractured reservoirs, it is common to represent the fractures as lower-dimensional inclusions embedded in the host medium. Existing discretizations of flow in porous media with thin inclusions assume that the principal directions of the inclusion permeability tensor are aligned with the inclusion orientation. While this modeling assumption works well with tensile fractures, it may fail in the context of faults, where the damage zone surrounding the main slip surface may introduce anisotropy that is not aligned with the main fault orientation. In this article, we introduce a generalized dimensional reduced model which preserves full-tensor permeability effects also in the out-of-plane direction of the inclusion. The governing equations of flow for the lower-dimensional objects are obtained through vertical averaging. We present a framework for discretization of the resulting mixed-dimensional problem, aimed at easy adaptation of existing simulation tools. We give numerical examples that show the failure of existing formulations when applied to anisotropic faulted porous media, and go on to show the convergence of our method in both two-dimensional and three-dimensional.publishedVersio

CityMobil: Human Factor Issues Regarding Highly-automated Vehicles on an eLane

In the European project ‘CityMobil’ the human factors aspects of (semi) autonomous driving are investigated. Systems in the car and in the driving environment enable the driver to drive (semi) automatically in a driving lane (eLane). One of the issues is the optimal interface for the change from automated to manual control and vice versa. Therefore, we conducted a driving simulator experiment with the aim to design and test the difference between a vocal and acoustic user interface, for a vehicle driven both manually and automatically. In the experiment the behavior of 24 drivers was observed, focusing on the transition of control and the occurrence of system errors. The performance of the transition of control was adequate for both interfaces at the beginning and ending of an eLane. In case of system failure, 15% of drivers failed to take timely control of the car for both interfaces. However if drivers regained control, they had a shorter response time to initiated the transfer of control to a manual mode with the vocal interface. Moreover, a subjective questionnaire showed that the vocal interface had a higher acceptance and perceived usability, than the acoustic interface. This study suggests that the vocal interface was preferred by the participants and can be recommended for the HMI of (semi) automated vehicles, especially when providing warnings about the system’s malfunctionin