My research interests include the analysis, numerical analysis and large scale computing necessary for solving partial differential equations that govern the evolution of fluid flows, broadly defined, including Newtonian, non-Newtonian, MHD, Boussinesq, and through porous media. A particular interest of mine is turbulent flow.
I am currently working on:
-- reduced order model development for high Reynolds number flows; current projects include using nonlinear filtering to localize
the regularization, with applications to Newtonian flows, MHD, and flows driven by natural convection.
-- algorithm development for efficient large scale computations for fluid flow problems; the focus here is typically how should a particular set
of PDEs be decoupled for efficient computations, but while maintaining a reasonable (or none at all) timestep restriction for stability and accuracy
-- approximate deconvolution turbulence modeling: model development, analysis, discretization methods
-- achieving long-time accuracy in fluid flow simulations by more closely aligning numerical discretizations with underlying
physics. A particular focus of this research is improving mass conservation and conservation of helicity.
-- velocity-vorticity-helicity (VVH) formulation of the Navier-Stokes equations; this formulation of the NSE was developed with my collaborator Maxim Olshanskii, and we believe it has the potential to lead to improved numerical algorithms for higher Reynolds number flows, particularly where the boundary layer effects are critical.