Research
I work on numerical methods for flows where the geometry moves: oscillating structures, deforming bodies, and the meshes that have to follow them. Most of my work builds high-order discontinuous Galerkin solvers in an arbitrary Lagrangian-Eulerian (ALE) setting, using the Galerkin-Boltzmann formulation for nearly incompressible flow, and runs them on GPUs. I also explore where machine learning can help, from physics-informed neural networks to hybrid reduced-order models.
A few results are below. Papers and talks are on the publications page.
An airfoil heaves up and down in a uniform stream and sheds a staggered street of counter-rotating vortices. The mesh follows the airfoil's motion in an ALE formulation, and the flow is computed with a high-order DG discretization of the Galerkin-Boltzmann equations. Color shows vorticity.
Read the preprint →A square body with an attached rod oscillates in a uniform stream. The flow separates from the body and forms an unsteady wake full of small-scale vortices along the rod, resolved here on a fine mesh that moves with the body. Color shows velocity magnitude.
Read the preprint →When a body bends, the surrounding mesh has to follow it without tangling. Here a physics-informed neural network solves the linear elasticity equations that move the mesh nodes, with the boundary motion enforced exactly by construction rather than through a penalty.
Read the paper →