Research

My research concerns development of accurate numerical methods for solving partial differential equations where parameters and solutions may be discontinuous across interfaces. These interfaces are typically moving. The main application I am working with is multiphase flows. Immiscible fluids, that may have different densities and viscosities, are separated by interfaces. At the interfaces surface tension forces act and surfactants (surface active agents) may be present, changing the surface tension. Surface tension effects and the discontinuities in the viscosity results in discontinuities in the pressure and the derivatives of the velocity field. How to accurately represent the singular surface tension force, the interface geometry, and solve the PDEs used to model multiphase flow phenomena are the questions I try to answer in my research.