The objective of this course is to equip students with the theoretical and computational foundations needed to model and simulate fluid flow in porous media, with a particular focus on reservoir rocks and subsurface applications.

More specifically, the course aims to:

• Introduce reservoir rock modeling, including the representation of petrophysical properties and geological heterogeneities;
• Present subsurface grid and mesh concepts, emphasizing structured, unstructured, and polyhedral grids;
• Develop mathematical models for single-phase flow, both incompressible and compressible;
• Study numerical methods and consistent discretizations for flow equations on general grids;
• Analyze and implement incompressible flow solvers, focusing on numerical stability and computational efficiency;
• Introduce multiphase flow modeling, including pressure–saturation coupling and compressibility effects;
• Explore the discretization of hyperbolic transport equations, which govern saturation fronts;
• Enable rapid prototyping of simulation models and solvers for research and practical applications.