Numerical methods that let a flow and the bodies inside it evolve together, show where and why a steady flow starts to break down, solve the large sparse systems behind incompressible flow efficiently, and model coupled multiphysics problems with particle-based solvers where fixed meshes fall short.
! Rigid and elastic bodies moving with a viscous flow, solved on one fixed grid. Immersed boundary and one-continuum formulations built on velocity–vorticity and vorticity–stream function variables, extended to full-Eulerian fluid–rigid–elastic systems and two-phase wave–body problems.
! Locating where instability begins. Energy gradient theory applied to two-fluid Poiseuille flow and Rayleigh–Taylor instability, and turned into a toolbox that maps the likely onset locus from a computed flow field.
! Krylov subspace solvers for the large sparse systems behind incompressible flow — preconditioning, storage schemes and high-order compact discretisations of Poisson's equation.
Particle-based solvers for problems where a fixed mesh breaks down — large deformation, free surfaces and coupled flow, heat transfer and material deformation. Applied to material flow and heat generation in friction stir welding and to SIMP-based topology optimisation of structures, and released as an open-source multiphysics solver.
