A coupled electro-thermo-mechanical FEM code for large scale problems including multi-domain and multiple time-step aspects

Abstract

This work concerns the development of a virtual prototyping tool for large scale electro-thermo-mechanical simulation of power converters used in railway transport including multi-domain and multiple time-steps aspects. For this purpose, Domain Decomposition Method (DDM) is used to give on one hand the ability to treat large scale problems and on the other hand, for transient analysis, the ability to use different time-steps in different parts of the numerical model. An Object-Oriented programming in C++ is used for the development of the application, allowing integration in a single interface, high evolutivity and code maintenance. Finally, parallelization is introduced to improve the performances of the code and obtain computing times compatible with industrial developments. In a first part, we present the formulation of DDM based on a dual approach in steady-state analysis including the building of the interfacial problem. Then, as presented by Combescure et al. we extend this formulation to multiple time-step transient analysis. The Euler semi-implicit scheme used to integrate first-order systems and the Newmark scheme used to integrate second order systems are detailed for both single time-step and multiple time-step computations. Then, we present a discussion concerning the choice of the continuity at the interface for first-order systems in single time-step and multiple time-step transient analysis. In the second part, the numerical implementation of the proposed approach in the FEM code DynELA is presented with a focus on the treatment of multi-physic aspects. Parallelization of the code on a Shared Memory Processors (SMPs) computer is achieved using the OpenMP programming standard. The last part of this work concerns the study of an industrial benchmark concerning the power converters: the electro-thermal simulation of a semi-conductor chip in transient analysis. This example allows to compare different strategies of tearing into subdomains and to couple different time-steps on the same structure.