BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eric Hester (University of Bath) DTSTART:20260224T130000Z DTEND:20260224T140000Z DTSTAMP:20260423T041234Z UID:UEA_mth/25 DESCRIPTION:Title: Automating Differential Geometry For Fluid Mechanics\nby Eric Hester (University of Bath) as part of Fluids and Structures Seminar @ UEA\n\n\nA bstract\nPhysical laws are coordinate-invariant\, but practical computatio ns are not. Good coordinates and frames can vastly simplify calculations\, speeding up numerical simulations as well as facilitating rigorous proofs . But this doesn't make them easy to use. Though the chain rule and vector calculus are sufficient in principle\, problems involving nonstandard geo metries\, curvilinear coordinates\, or moving interfaces can rapidly spira l in complexity. Coordinate expansions become a major source of errors and lost time. Computer algebra systems help\, but functionality for general geometries isn't "out-of-the-box". Other higher-level packages like xAct a re powerful\, but are often designed for index calculations in general rel ativity rather than typical continuum-mechanics PDEs with boundaries and c onstraints. There is a missing middle of tools to automatically convert sy stems of PDEs on nonstandard geometries to their concrete component forms. \n\nI will introduce a small Mathematica package\, Tensors\, that aims to close this gap. Given coordinate mappings\, tensor fields\, frames\, and m etrics on manifolds and their boundaries\, the package automatically trans lates expressions composed of standard differential operators and geometri c data (e.g. gradients\, integrals\, curvatures\, normals etc.) into compo nent form. Automating this conversion makes complex geometric calculations faster\, more reproducible\, and easier to generalise. I will illustrate with an application from multiphase fluid dynamics\, showing how the packa ge streamlines geometric constructions needed for high-order asymptotics\, leading to better-conditioned\, complexity-optimal solvers for free-bound ary problems.\n LOCATION:https://researchseminars.org/talk/UEA_mth/25/ END:VEVENT END:VCALENDAR