Unstructured Higher Resolution Convective Schemes for Flow in Porous Media

Novel high resolution schemes for convective flow approximation are developed and coupled with general continuous full-tensor Darcy flux approximations. This development leads to new locally conservative formulations for multiphase flow in porous media.<br><br>The higher order schemes are designed for fluid transport on unstructured grids and are constructed using slope limiters such that they are stable with a maximum principle that ensures solutions are free of spurious oscillations. The schemes are developed to handle unstructured meshes with variable grid spacing and different formulations are compared.<br>Benefits of the resulting schemes are demonstrated for classical test problems in reservoir simulation including cases with full tensor permeability fields. The test cases involve a range of unstructured grids with variations in grid spacing, orientation and permeability that lead to flow fields that are poorly resolved by standard simulation methods. The new formulation is compared with standard reservoir simulation schemes and control-volume finite element methods. The new schemes are shown to effectively reduce numerical diffusion while resolving flow induced by rapid changes in permeability, leading to superior resolution of concentration and saturation fronts compared to other schemes.