Multi scale strategies for EMC modelling – M2CEM

More and more applications in electromagnetic compatibility require to take into account very small elements in the geometry for a correct evaluation of electromagnetic interactions. We are particularly interested in this project in a problem dimensioning in aeronautics, which is the risk of electrical breakdown resulting from a high amplitude current injection (example of lightning), in the areas of overlap by riveting panels constituting the structure. More concretely, one wonders what would be on an aircraft the potential points of electrical breakdown. These breakdowns are indeed sources of degradation of the structure and generators of disturbances or even initiation of fires or explosions in sensitive areas.
Today, a simulation of this problem is a real challenge because there is no effective method taking into account both the 3D geometric extent and the local details related to these risk areas. Indeed, to simulate the problem it is necessary to know globally the distribution of currents and surface fields over the entire 3D structure, but also around the inter-panel space in the overlap areas. Despite the fact that we can locally refine a mesh in the current GD schemes, we note, for our problem, that the number of zones to be refined and the size of the detail to be taken into account in these zones require massive multi-scale meshes) that make current solutions too expensive or even inadequate. It is therefore important to consider this multi-scale aspect for global geometry and to propose efficient solutions in cost calculation, in memory load and in precision to correctly overcome the problem. In this project, to have an operating solution, it is necessary to make improvements to the current GD approach, but also to have a good mesh generation strategy for the simulation in terms of calculation costs. This is why we are interested in the following 2 scientific challenges:
- The study of methods or diagrams that allow to improve the GD approach in terms of calculation and memory cost to be able to deal with applications where we have to consider several mesh zones with an important scale factor. We then obtain non-compliant hp meshes in which the calculation of the fluxes at the interfaces of the different mesh areas is very expensive and the time step for the stability of the numerical scheme becomes too small. We will therefore look for inexpensive approaches for the calculation of flows at the interfaces of refinement zones and temporal schemes based on stable local time step methods, able to take into account large variations in time steps (greater than 10 or 100) or schemes without CF or locally implicit time;
- In order to perform the simulation, it will then be necessary to have a strategy to define an optimal mesh in terms of calculation and memory cost with our improved GD solution. In particular, it will be necessary to be able to define cartesian and unstructured meshing areas according to the geometry under study, such as the number of Cartesian cells and the size of the cells being maximized, while maintaining the stability of the GD scheme. In addition, for some unstructured areas it will be necessary to define local refinements able to handle small details, while ensuring the stability and consistency of the improved GD approach.

The solutions proposed in the two previous points, will be validated and quantified on an example of small size by comparison with current solutions.