Discontinuous finite element methods for the simulation of rotating electrical machines

Abstract

The capability of discontinuous finite element methods of handling non-matching grids is exploited in the simulation of rotating electrical machines. During time stepping, the relative movement of two meshes, consistent with two different regions of the electrical device (rotor and stator), results in the generation of so-called hanging nodes on the slip surface. A discretisation of the problem in the air-gap region between rotor and stator, which relies entirely on finite element methods, is presented here. A discontinuous Galerkin method is applied in a small region containing the slip surface, and a conforming method is used in the remaining part

Efficient use of the local discontinuous Galerkin method for meshes sliding on a circular boundary

“…In this paper, the basics of the coupled LDG/continuous FE method are reviewed, and its performance is compared with the one of an existing FEM/BEM code [13] on the TEAM24 benchmark problem. This extends the preliminary investigation presented in [7].…”

“…For this reason, FE methods are usually coupled with other techniques that do not require a mesh in the air-gap between rotor and stator (BEM, Fourier series expansion), or they are modified or enhanced in some way to restore potential continuity (Lagrange multipliers, partial remeshing, overlapping elements) [1]- [6]. In this work, an alternative approach that was first introduced in [7], which relies entirely on FE methods, is used.…”

Local discontinuous Galerkin methods for elliptic problems

“…The corresponding coupled method, introduced in Reference [12] and analysed in Reference [11], combines the ease with which the LDG method handles hanging nodes with the lower computational cost of standard conforming ÿnite elements. This approach is also very promising in the context of multi-physics or multi-material problems, where the practitioner might want to use a DG method only in certain parts of the computational domain.…”

“…The advantage of applying the LDG method to elliptic problems relies on the ease with which it handles hanging nodes, elements of general shapes, and local spaces of di erent types; these properties render the LDG method ideally suited for hp-adaptivity and allow it to be easily coupled with other methods. Indeed, the coupling of LDG methods with conforming ÿnite elements (and the performance of the resulting method in the presence of meshes with hanging nodes) is analysed and numerically tested in Reference [11]; the motivation for this coupling comes from an application in the framework of rotating electrical machines, see Reference [12]. An extension of the LDG method to the Stokes system, where the discretization of the divergence-free condition on the velocity is the main di culty, was proposed and analysed in Reference [13].…”

Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

“…Finally, the coupling of DG methods with other methods seems attractive in some circumstances. See Alotto et al [1] and Perugia and Schötzau [60].…”