High order numerical methods for multiphysics couplings

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The project results in the development of high order discontinuous Galerkin methods for complex flow and transport problems. The investigator analyzes and numerically studies different types of couplings, such as the coupling of Stokes or Navier-Stokes equations with miscible displacement and multiphase flow. Physically meaningful conditions are imposed at the interface between surface region and subsurface region. The mathematical advances in numerical analysis consist of proving existence and uniqueness of high order solutions of coupled systems and of rigorously deriving a priori error estimates with respect to the mesh size and the polynomial degree. Verification of the numerical solutions is performed through convergence studies, adaptivity with respect to the mesh size and the polynomial degree and comparisons with solutions obtained from other discretization techniques. A computational framework valid for two and three-dimensional problems is developed.This work deals with the modeling, analysis and simulation of multiphysics problems arising for instance in groundwater contamination through rivers and lakes. Groundwater becomes contaminated when human-made substances or sometimes naturally occurring substances are dissolved in waters recharging the groundwater. Often, as groundwater is connected with lakes and rivers, the pollution of these surface waters implies the pollution of aquifers. The investigator studies the interaction between surface flow and subsurface flow. Accurate and efficient numerical methods are developed and analyzed. Intensive numerical simulations and comparison with experimental data allow gaining further knowledge on multiphysics couplings. The interdisciplinary nature of the task fosters transfer of scientific knowledge across the engineering and science communities.This project advances discovery and understanding while promoting learning by training several graduate students and undergraduate students. An important educational activity is a week-long Summer Math School offered to high-school students entering grades 10-12. The event?s objective is to encourage students to pursue a career in science and mathematics.