Research interests
Numerical methods for reaction-diffusion systems
- Pattern formation in reaction-diffusion systems. (simulations),
- Solving advection-reaction-diffusion equations on mapped two dimensional surface grids (more info, simulations),
- Runge-Kutta Chebyschev schemes for explicit integration of reaction-diffusion equations,
Finite volume schemes for mapped grids
- Grids for the disk and sphere that have desirable properties for explicit finite volume schemes (more info),
Models for disperse multiphase flow and transport on the sphere
- Shallow water wave equations on the sphere (article)
- Approximate Riemann solver for disperse water-vapor-air mixtures
- Tracer transport in the atmosphere (more info)
Adaptive mesh refinement and software frameworks
- Adaptive mesh refinement methods for solving PDEs on logically Cartesian meshes,
- Software frameworks for solving PDEs on adaptively refined meshes. ( AMR software packages),
Immersed interface methods, embedded boundary methods and cut-cell methods
- Immersed interface methods for Navier-Stokes (more info)
- Cut-cell finite volume scheme for advection-diffusion in complex geometry (more info)
Dendritic crystal growth
- Solving the phasefield equations on mapped grids (simulations)
- Far-field boundary conditions for the heat-equation (more info)
Computer graphics and visualization
- Suite of Matlab routines for plotting results from 1d, 2d and 3d Clawpack routines (ClawGraphics).
- Ray tracing (CSE 557 project)
Last modified: Mon May 21 14:28:48 CEST 2012