- Soft hydraulics: Towards a predictive theory of the static and dynamic response of compliant flow conduits.
- Fluid–structure interactions in intracranial aneurysms: Coupled flow and biomechanics.
- Continuum models and numerical methods for particle-laden multiphase flows in complex and 3D geometries (see twoFluidsNBSuspensionFoam project).
- Interfacial fluid mechanics and (in)stability of fluid–fluid interfaces in the presence of multiphysics interactions.
- Non-Newtonian fluid flows, including viscous gravity currents, start-up problems, microflows & slip.
- Nonlinear waves; PDEs with Hamiltonian structure; stochastics (see e.g., langevinkinks project).
- Hyperbolic conservation laws in fluid mechanics.
- Anomalous scalings in the diffusion of granular materials; long-time asymptotics of diffusion equations.
- Chaotic mixing of granular materials; 3D nonlinear dynamical systems and chaos.
- Nonlinear Fourier analysis and transforms for ocean acoustics modeling (NONFATFOAM).
- Nonlinear acoustics (inviscid and thermoviscous) and shock formation.
- Hyperbolic heat conduction and wave propagation.
- Wavelets and wavelet methods for signal processing and solution of PDEs.