This project builds on the work done on using the Discontinuous Galerkin method to solve advection dominated flow problems. While Discontinuous Galerkin methods have been shown to address the problem of oscillations and the development of interior and boundary layers (referred to as the Gibbs phenomenon) associated with simulations involving high Peclet numbers, they are implemented at the cost of a significant increase in the degrees of freedom, which makes them prohibitively expensive for upscaling to large scale problems.

This project focuses on implementing an Interface Stabilized Discontinuous Galerkin method that involves solving a linear system that has the same number of degrees of freedom as that of a continuous Finite Element method, while retaining the advantage of providing stable solutions for advection dominated flow problems. The solver is programmed in a Python and C++ finite rlement solver called FEniCS, developed by Simula Research Laboratories, Norway, and is tested on a computational fluid dynamics problem, which simulates the change in drug concentration injected in the Cerebrospinal fluid in a mesh of the cervical Spinal Subarachnoid Space.