AS1.1. SPARSE LINEAR ALGEBRA – DISCRETIZATION AND FINITE ELEMENTS – OPTIMISATION
Numerical algorithms, solvers, and discretization techniques form the foundation of scientific computing and are essential across all areas of computational science and engineering. At CERFACS, maintaining and enhancing expertise in these domains is a strategic priority, as many physical and engineering problems rely on solving partial differential equations (PDEs). Efficient numerical solvers are not only vital for PDEs but also for tasks involving integral equations, stochastic models, optimization, and data assimilation. CERFACS aims to remain at the forefront of scientific computing by developing forward simulation methods and addressing complex inverse problems. These challenges often involve intricate geometry, mesh generation, parallel processing, and load balancing, necessitating robust and distributed data structures. The goal is to sustain a broad mathematical expertise that supports diverse applications while also conducting deep research in numerical algorithms and computer science. To remain competitive in publishing and innovation, CERFACS must balance this breadth with depth. Research efforts will be prioritized to align with strategic partnerships and application needs, positioning CERFACS as a vital link between advanced academic research and the real-world computational problems faced by its stakeholders. This dual focus ensures relevance both in academic excellence and practical impact.
AS1.2. NOVEL NUMERICAL APPROACHES APPLIED TO CFD (LBM & HOM)
Computational Fluid Dynamics (CFD) has traditionally focused on modeling turbulent flows, but the rise of massively parallel computing and unsteady simulation capabilities has shifted the emphasis toward directly simulating parts of turbulent flows with fewer modeling assumptions. This approach improves predictive accuracy in real-world applications while maintaining acceptable computational cost. To meet these challenges, CFD solvers must deliver unsteady, accurate simulations on complex geometries efficiently. Two promising methods—Lattice Boltzmann Method (LBM) and High-Order Methods (HOM)—offer significant advantages over traditional approaches. LBM, which has seen extensive development at CERFACS over the past six years, is easily parallelizable and well-suited for complex geometries via octree meshes. It also supports multiphysics modeling and has shown success in areas such as turbulence, multiphase flows, aeroacoustics, compressible flows, and high-performance computing. Further expansion of LBM research into applications like rotating machinery is planned. Meanwhile, HOMs provide high-fidelity simulations with greater robustness to mesh quality and resolution, making them ideal for unstructured mesh environments typical in industrial settings. By reducing computational time and improving accuracy, both LBM and HOM represent strategic opportunities for advancing unsteady flow simulations and meeting the evolving needs of scientific and industrial applications.
