Reduced order field-circuit modeling of squirrel cage induction machines for automotive applications

Purpose The aim of the paper is to investigate the impacts of simplifications of a reduced-order simulation model of squirrel cage induction machines (SCIMs) by numerical experiments. Design/methodology/approach Design of setups to isolate the main influences on the results of the reduced-order model of SCIMs. Results of time-stepping finite element calculations are used as benchmark. Findings Whereas neglecting eddy current effects and the assumption of a sinusoidal rotor current distribution leads to acceptable deviations in regular inverter operation, the sampling and interpolation of the machine parameters in a two-axis coordinate system considerably deteriorate the model accuracy. Using a polar coordinate system for this purpose is expected to significantly improve the model quality. Originality/value Preparing the ground for a successful, both fast and accurate simulation model of SCIMs as parts of electrified drivetrains.

Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains

This article is concerned with the discretisation of the Stokes equations on time-dependent domains in an Eulerian coordinate framework. Our work can be seen as an extension of a recent paper by Lehrenfeld and Olshanskii (ESAIM: M2AN 53(2):585–614, 2019), where BDF-type time-stepping schemes are studied for a parabolic equation on moving domains. For space discretisation, a geometrically unfitted finite element discretisation is applied in combination with Nitsche’s method to impose boundary conditions. Physically undefined values of the solution at previous time-steps are extended implicitly by means of so-called ghost penalty stabilisations. We derive a complete a priori error analysis of the discretisation error in space and time, including optimal $$L^2(L^2)$$ L 2 ( L 2 ) -norm error bounds for the velocities. Finally, the theoretical results are substantiated with numerical examples.

Stationary multi-kinks in the discrete sine-Gordon equation

We consider the existence and spectral stability of static multi-kink structures in the discrete sine-Gordon equation, as a representative example of the family of discrete Klein–Gordon models. The multi-kinks are constructed using Lin’s method from an alternating sequence of well-separated kink and antikink solutions. We then locate the point spectrum associated with these multi-kink solutions by reducing the spectral problem to a matrix equation. For an m-structure multi-kink, there will be m eigenvalues in the point spectrum near each eigenvalue of the primary kink, and, as long as the spectrum of the primary kink is imaginary, the spectrum of the multi-kink will be as well. We obtain analytic expressions for the eigenvalues of a multi-kink in terms of the eigenvalues and corresponding eigenfunctions of the primary kink, and these are in very good agreement with numerical results. We also perform numerical time-stepping experiments on perturbations of multi-kinks, and the outcomes of these simulations are interpreted using the spectral results.

Irksome: Automating Runge–Kutta Time-stepping for Finite Element Methods

While implicit Runge–Kutta (RK) methods possess high order accuracy and important stability properties, implementation difficulties and the high expense of solving the coupled algebraic system at each time step are frequently cited as impediments. We present Irksome , a high-level library for manipulating UFL (Unified Form Language) expressions of semidiscrete variational forms to obtain UFL expressions for the coupled Runge–Kutta stage equations at each time step. Irksome works with the Firedrake package to enable the efficient solution of the resulting coupled algebraic systems. Numerical examples confirm the efficacy of the software and our solver techniques for various problems.