MFA II: Modelling, numerics, and inference

Computer simulations of flowing gases can produce physically impossible results – negative densities, energy appearing from nowhere – if the underlying numerical methods are not carefully designed. This mathematics project develops simulation methods that provably respect the laws of physics at every step. Three threads come together: numerical schemes that stay reliable across widely different flow regimes, AI-assisted tuning of the models that stand in for unresolved small-scale turbulence, and a thermodynamically rigorous recipe (the "GENERIC" formalism) for systematically simplifying detailed equations into coarser ones – applied to the mixture of cold gas clouds and hot magnetized plasma around galaxies. It is multi-scale because it addresses the unresolved scales problem from three complementary directions, and interdisciplinary because applied mathematicians develop the theory hand in hand with astrophysicists who need it for galaxy and accretion-disk simulations.