Multi-physics problems computation using numerically adapted meshes: application to magneto-thermo-mechanical systems

In physical systems, interactions between phenomena of different nature, generally coupled to each other, are often involved. Their comprehensive study requires the use of various physical models sharing a unique set of physical quantities. In an effort to correctly model these systems, numerical methods are frequently used. However, computational tools dedicated to such a specific scope of use are barely available. Furthermore, unsuited numerical discretization and high memory costs are two major drawbacks limiting the use of coupled numerical models. We present in this paper a global method which enables the independent use of existing computational tools, the numerical adaption to each physical model and the reduction of the memory use. This method has resorted to a unique discretization and topology for each physical model. The link between these independent models is ensured by the projection of quantities common to them. Thus computational tools, originally not intended to operate together, can be used again. After a theoretical description of the projection method, we will present successive application to discretizations of different nature. Thus, numerical efficiency of the projections in themselves will be tested. Because of the large range of combination of physical models, additional tests will be carried out in order to determine the most accurate coupling flowchart. A highly coupled problem, involving three different physical models, will be presented using the projection method. Results show a significant gain in flexibility and cuts in memory costs. Present test-cases reveal that accuracy is of same order as the one obtained using dedicated tools.