AbstractThis work presents a new fully-unstructured meshing scheme for generating simulation meshes, coupled with a novel simulation method for fluid flow models in porous media.We use unstructured tetrahedral meshing algorithms to generate meshes that rigorously adhere to structural and depositional heterogeneity in geological reservoir models at multiple scales. Geological heterogeneity is represented using numerous surfaces, in contrast with traditional pixel- or grid-based methods. This approach allows the generation of meshes which capture heterogeneity more efficiently and accurately than structured or partially-structured grids.The flow simulations are performed using a new hybrid discontinuous Galerkin/control volume based method which combines continuous pressure and discontinuous velocities. Our approach rigorously enforces material balance equations while ensuring crucial scalar fields such as pressure and saturation remain positive and bounded.This research has direct application to aquifer fl...