The associate team GEM3 is focussed on development of multiscale numerical methods for linear and nonlinear elliptic and parabolic PDE arising from the applications to surface and subsurface geophysics. Both teams have a long standing expertise in mathematical and numerical modeling of complex geological environments, including modeling of multi-phase non-isothermal flows in fractured and faulted reservoirs and the modeling of coupled flow and geomechanics processes. Their applications cover a wide range, from managing freshwater and geothermal resources to CO2 and H2 storage and nuclear waste storage safety assessment.
In this genuine multidisciplinary field, LNCC has a well-established collaboration network that includes several academic institutions in Brazil, such as UFPE, UFPB, UFC, and UFSC, as well as industrial partners like PETROBRAS and TotalEnergies Brasil. Additionally, Team GALETS has established long-term partnerships with BRGM, ANDRA, Storengy, and IFPEN, and is actively involved in the PEPR Sous-sol, PEPR MathVives, and the ANR project EARTH-BEAT. Since 2020, LNCC has been collaborating with the French team on the JCJC ANR project Top-up, which addresses the numerical flood simulations in complex urban environments using multiscale and domain decomposition methods.
The expertise of the two teams in multiscale modeling and methods is complementary. Over the past decade, LNCC has focused on the development and analysis of its original Mixed Hybrid Multiscale (MHM) method, which has been successfully applied to various linear elliptic or parabolic problems, including singularly perturbed convection-reaction-diffusion, elasticity, Stokes-Brinkman, and wave propagation problems.
The French team's work on multiscale discretizations began with the ANR project Top-up, which focuses on urban flood modeling using the Diffusive Wave model, combined with high-resolution data. For flow problems in domains with numerous polygonal obstacles, the team has developed a new multiscale Trefftz method and error analysis tools that provide robust estimates for geometry induced singularities. Additionally, the French team has gained expertise in combining multiscale methods with both linear and nonlinear domain decomposition.