Fluid Dynamics

Our interest in fluid dynamics is in problems with evolving free boundaries, such as shock/detonation waves and their stability, hydraulic jumps and their stability, non-linear waves in free-surface fluid flows.

Numerical Simulations

Our primary focus is on developing high-order shock-fitting methods for problems of multi-dimensional detonation propagation. The phenomenon of detonation poses significant challenges for numerical methods due to very complex instabilities that are inherent to detonation shocks. Very careful resolution of shock propagation is necessary to capture these instabilities. In addition, we also work on algorithms and numerical simulations of systems of reaction-diffusion equations and dispersive PDE.

Applied Partial Differential Equations

Our group's efforts are focused on the study of partial differential equations with particular emphasis on traveling wave solutions, their stability and nonlinear dynamics, asymptotic decay of stable solutions, and existence of attractors. Our primary interest is in hyperbolic PDE and shock waves.