Global-Local ROM for the solution of parabolic problems with highly concentrated moving sources

Problems characterised by steep moving gradients are challenging for any numerical technique and even more for the successful formulation of Reduced Order Models (ROMs). The aim of this work is to study the numerical solution of problems with steep moving gradients, by placing the focus on parabolic problems with highly concentrated moving sources. More specifically, a Global-Local scheme well-suited for reduction methods is formulated. With this Global-Localscheme, the local nature of the steep moving gradients is exploited by modelling the neighbourhood of the heat source with a moving local domain. This domain is coupled to the global domain without requiring any re-mesh and preserving the meshes of both domains during the whole simulation. Then, a ROM based on the Proper Orthogonal Decomposition (POD) technique is developed for the moving local domain. The proposed technique establishes a valid approach for tackling the non-separability of the space and time dimensions of these problems. In order to assess the numerical performance of the proposed numerical techniques, several evaluation tests are performed.