Computational methods and tools

Mathematical and computational modelling relies on methods and tools providing numerical solutions to complex simulation problems. These techniques range from the pre-processing (CAD interface, automatic meshing, data acquisition…) to verification and validation via a posteriori error assessment and adaptivity, showcasing a diversity of state-of-the-art solvers. We aim at designing and implementing efficient methodologies producing high-fidelity solutions with certified accuracy, adapted to each particular problem under analysis. We develop these innovative methodologies both in academic codes (with flexibility to intrusively test new ideas) and professional or commercial codes, certified by our industrial partners, with a large variety of models and methods, extensively tested and computationally optimized. In the latter case we aim at using non-intrusive implementations. The problems under consideration cover a wide range of applications:

• Engineering design (fluids): flow and wave problems, drag and lift automotive optimization, aeroacoustics, zero-gravity flows…
• Engineering design (structural and coupled): parametric solvers for structural mechanics and dynamics with automotive applications, crashworthiness, structural vibrations and NVH analysis…
• Manufacturing processes and system monitoring: real-time simulation with data assimilation
• Patient-specific modelling and simulation o clinical procedures and analyses, supporting decision making
• Energy related problems: CFD analysis for the location of wind turbines, reservoir simulation, electricity networks, acoustic impact of power plants, prospection of deep geothermal resources…

In the framework of seeking real-time responses to multiparametric problems, we are particularly concerned with the efficiency of the numerical methodologies and the credibility of the solutions provided. Thus, from a methodological viewpoint, the current ongoing research includes:

• High-fidelity simulations: high-order approximations (in particular HDG formulations) with exact geometrical descriptions (NEFEM)
• Reduced order models (viz. PGD, POD, kPOD…) for generalized parametric solutions
• C0 Interior Penalty Methods for 4th order partial differential equations
• Data assimilation and data-driven models
• Uncertainty quantification and model updating with goal-oriented error assessment and adaptivity
• Automatic generation of high-order meshes