My research interests include high order structure-preserving numerical methods for fluid, kinetic and multi-scale models. Specific topics include:
- High order low rank tensor approach for transport PDEs and kinetic models with local conservation and structure preservation.
- Eulerian-Lagrangian high order Runge-Kutta discontinous Galerkin methods.
- High order semi-Lagrangian method for kinetic and transport equations with applications in astrophysics, plasma Physics and meteorology.
- Asymptotic preserving numerical methods for multi-scale PDEs.
- High order methods for temporal multi-scale problems: implicit-explicit Runge-Kutta method and integral deferred correction method for singular perturbation problems.
The application areas include:
- Computational fluid dynamics.
- Kinetic simulations and applications to Plasma physics.
- Climate modeling and simulations.
- Traffic flow simulations.