My recent research interests have been on the developing high-order accurate numerical methods for solving
partial differential equations, specially for equations related to convection dominated
flow phenomena (e.g. Euler equations,
Navier-Stokes equations), scientific computing, and computational math-biology.
I am currently working on:
- Blood flow modeling
- Conservative front tracking.
- Modeling blood thrombus formation in the blood vessel with a multiscale model which couples
stochastic discrete Cellular Potts Model with continuum PDE model such as Navier-Stokes equations
for the blood flow and convection-diffusion-reaction equations for coagulation reactions.
- Modeling P. aeruginosa (a bacterium) swarm pattern formation. The model couples thin liquid film model
with stochastic discrete off-lattice model for individual cells.
- Discontinuous Galerkin methods for solving conservation laws.
- Clot (geomview files)