Mathematics

Computational fluid dynamics (CFD) is an integral component of research and engineering in fluid mechanics, providing unrivalled levels of fidelity and detail compared to theory and experiment. Three of the core elements of CFD that govern the progress of its development and utility are: 1) developing advanced mathematical models to properly capture the necessary physics for a given problem; 2) implementing advanced methods and algorithms to ensure efficient execution on modern high-performance computing (HPC) systems; 3) applying advanced data-driven analysis to inform decision making and solve real-world problems. This talk will give a selective overview of recent research activities covering these areas, including the development of a flexible fluid-structure interaction solver for violent free-surface flows, accelerated particle-based simulations with graph neural networks, Bayesian optimisation of wall-normal blowing control for skin-friction drag reduction in turbulent boundary layers, and large-scale uncertainty quantification campaigns of scale-resolving simulations. Together, these examples cover a broad range of topics – such as different discretisation schemes, HPC architectures, and real-world applications – and demonstrate the power of CFD to tackle complex problems across fluid mechanics. Finally, the talk will conclude with a perspective on current research trends in CFD and a look ahead to potential future research directions.