His research has focused on developing numerical algorithms for hydrodynamics and magnetohydrodynamics, implementing them on vector and parallel computers, and applying them to studies of the Sun, as well as to other areas of plasma science. His algorithms and software for obtaining accurate, robust, and flux-conserving solutions to the MHD equations, in particular, are in wide use by colleagues at NASA, across the US, and around the world. He has applied these numerical tools to the slowly evolving, large-scale solar magnetic field and to dynamical events at smaller scales.