On a multiscale strategy for parametrized strongly coupled thermo-poroelasticity problems

Most industrial systems involve physical phenomena of sundry kinds (mechanical, thermal, chemical, electromagnetic, etc.), which can evolve in a strongly coupled manner, meaning that there is a mutual interaction between at least two physics. This study focuses on simulating strongly coupled thermo-poroelasticity problems and handling coupling between solid mechanics, fluid mechanics, and thermics. Such multiphysics problems present different time and space scales depending on the physics considered. It has been observed that fluid phenomena occur on small time scales while thermal phenomena are visible on much larger ones. Therefore, to reduce the computational costs, it is beneficial to choose time discretizations adapted to each physics. Likewise, using different meshes for each physics could be considered. The method used in this work for solving strongly coupled Multiphysics problems is the LATIN-PGD method. This non-incremental iterative approach uses model order reduction techniques, reducing the computational costs while preserving high accuracy. The method appears particularly suitable for parametrized studies used in optimization problems. Moreover, the modularity of the LATIN-PGD solver presents advantages when dealing with multiphysics problems thanks to the concept of interface between physics. This contribution extends the work presented in to nonlinear problems involving three physics. The solver was validated on an academic test case. The approach has then been applied to an industrial application focusing on ceramic membranes with three-dimensional models. For both examples, the strategy used to tackle parametrized studies greatly reduces computation times compared to a naive approach. For instance, a gain in time of 20 was observed when running 343 simulations with material variability in the industrial example. The next part of the work deals with the multiscale aspects of the multiphysics problems. Each physics has its time discretization and its mesh to refine the discretizations where needed only. The interface between physics plays the role of an adaptive space between the different discretizations. We use different time discretizations in the academic example and different meshes in the industrial one. Future work will combine data-based physics with model-based one.