In low Mach number aeroacoustics, the known disparity of length scales makes it possible to apply well‐suited simulation models using different meshes for flow and acoustics. The workflow of these hybrid methodologies include performing an unsteady flow simulation, computing the acoustic sources, and simulating the acoustic field. Therefore, hybrid methods seek for robust and flexible procedures, providing a conservative mesh to mesh interpolation of the sources while ensuring high computational efficiency. We propose a highly specialized radial basis function interpolation for the challenges during hybrid simulations. First, the computationally efficient local radial basis function interpolation in conjunction with a connectivity‐based neighbor search technique is presented. Second, we discuss the computation of spatial derivatives based on radial basis functions. These derivatives are computed in a local‐global approach, using a Gaussian kernel on local point stencils. Third, radial basis function interpolation and derivatives are used to compute complex aeroacoustic source terms. These ingredients are necessary to provide flexible source term calculations that robustly connect flow and acoustics. Finally, the capabilities of the presented approach are shown in a numerical experiment with a co‐rotating vortex pair.

In this work, the reduced scalar potential is utilized to derive a finite element formulation capable of handling hysteretic nonlinear material laws. The Fréchet derivative is employed to deduce a quasi-Newton scheme in the weak form for solving the nonlinear partial differential equation that describes the magnetostatic field. Methods for evaluating the Jacobian are presented, and their performance is compared on a 3-D domain under uniaxial and rotational excitation. The numerical results demonstrate the necessity of a flexible approximation to overcome the non-uniqueness of the Jacobian at reversal points, which naturally occurs in hysteresis loops. Consequently, an exact or excessively localized evaluation would give rise to difficulties in states of material magnetization characterized by these reversal points.

Purpose: The purpose of this paper is to examine a solution strategy for coupled nonlinear magnetic-thermal problems and apply it to the heating process of a thin moving steel sheet. Performing efficient numerical simulations of induction heating processes becomes ever more important because of faster production development cycles, where the quasi steady-state solution of the problem plays a pivotal role. Design/methodology/approach: To avoid time-consuming transient simulations, the eddy current problem is transformed into frequency domain and a harmonic balancing scheme is used to take into account the nonlinear BH-curve. The thermal problem is solved in steady-state domain, which is carried out by including a convective term to model the stationary heat transport due to the sheet velocity. Findings: The presented solution strategy is compared to a classical nonlinear transient reference solution of the eddy current problem and shows good convergence, even for a small number of considered harmonics. Originality/value: Numerical simulations of induction heating processes are necessary to fully understand certain phenomena, e.g. local overheating of areas in thin structures. With the presented approach it is possible to perform large 3D simulations without excessive computational resources by exploiting certain properties of the multiharmonic solution of the eddy current problem. Together with the use of nonconforming interfaces, the overall computational complexity of the problem can be decreased significantly.

In this paper, a methodology to incorporate non-conforming interfaces between several conforming mesh regions is presented for Maxwell’s curl-curl problem. The derivation starts from a general Interior Penalty Discontinuous Galerkin formulation of the curl-curl problem and eliminates all interior jumps in the conforming parts but retains them across non-conforming interfaces. Therefore, it is possible to think of this Nitsche approach for interfaces as a specialization of Discontinuous Galerkin on meshes, which are conforming nearly everywhere. The applicability of this approach is demonstrated in two numerical examples, including parameter jumps at the interface. A convergence study is performed for h-refinement, including the investigation of the penalization-(Nitsche-) parameter.