Georgia Institute of Technology College of Sciences

New technologies have been introduced into the front tracking method to improve its performance in extreme applications, those dominated by a high density of interfacial area. New mathematical theories have been developed to understand the meaning of numerical convergence in this regime. In view of the scientific difficulties of such problems, careful verifaction, validation and uncertainty quantification studies have been conducted. A number of interface dominated flows occur within practical problems of high consequence, and in these cases, we are able to contribute to ongoing scientific studies. We include here turbulent mixing and combustion, chemical processing, design of high energy accelerators, nuclear fusion related studies, studies of nuclear power reactors and studies of flow in porous media. In this lecture, we will review some of the above topics.