Mathematical and computational modeling 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, and include a diverse population of solvers. Our goal is to design and implement efficient methodologies to obtain 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. This program is organized into three groups: “Credible high-fidelity data-driven models”, “Automatic and adaptive meshing with error assessment” and “CFD with industrial codes”.
The problems under consideration cover a wide range of applications:
• Engineering design: flow and wave problems, drag and lift automotive optimization, aeroacoustics, zero-gravity flows,…
• Manufacturing processes: real-time simulation with data assimilation.
• Architectured materials: parametric micro structures for specific macro properties.
• Patient-specific modeling and simulation,
• Energy related problems: CFD analysis for the location of wind turbines, reservoir simulation, electricity networks, acoustic impact of power plants,…
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) for generalized parametric solutions,
• Data assimilation and data-driven models,
• Uncertainty quantification and model updating for reliable simulations with goal-oriented error
assessment and adaptivity,
• Automatic generation of high-order meshes.
A. Huerta, A. Garcia,
J. Sarrate, N. Pares
A. de Montlaur