Research Areas : Computational and Applied Mathematics, Computational Fluid Dynamics, Interface Dynamics, Partial Differential Equations, Numerical Analysis
My research interests involve the development of efficient and accurate numerical algorithms to solve fluid dynamics and multi-physics problems. In particular, I have focused on the development of all speed multi-phase flow algorithms, semi-implicit adaptive mesh refinement methods for underwater explosions and implosions, higher order accurate auxiliary variable projection methods for zero-Mach gas dynamics, interface tracking (hybrid marker-level set) methods, multi-physics coupling problems in nuclear reactors, self-consistent IMplicit/EXplicit (IMEX) methods for variety of fluid dynamics and multi-physics applications, the Jacobian-Free Newton Krylov (JFNK) methods for non-linear problems, point implicit methods (PIM) for slow transient and steady state problems that occur in nuclear applications, well-posed two-phase seven equation flow models for reactor thermal-hydraulics applications, highly accurate (space and time) numerical methods for compressible fluid dynamics applications, and recently effective preconditioning strategies within the JFNK framework to accurately simulate brain tumor problems.