Control Volume Discretisation on Non-Matching Meshes in 3D

Abstract

Complex geometric and geological features of realistic reservoirs motivate the need for flexible and robust flux discretisation for forecasting of fluid flow in porous media. Geo-modelling tools allow faults in the stratigraphy and local grid refinements which typically result in non-matching meshes with hanging nodes. Flow simulations based on cell centred control volume discretisations can be performed when connectivities are established and transmissibilities are computed across the non-matching interfaces. Ideally, the interface couplings should be in a form that allows the use of robust flux discretisation techniques. Existing approaches for such problems include generating prismatic ghost cells along the non-matching interfaces or deriving specialised stencils for possible mesh configurations.<br>We study an alternative technique that deals with non-matching meshes by combining a conversion to a topologically conforming mesh with a general O-method multi point flux approximation. Hanging-nodes are removed by adding them to the mesh interfaces, creating general polyhedral mesh cells. Then the general point-based algorithm for setting up O-method interaction regions is used.<br>Since, in three dimensions, this approach can lead to a mismatch between the number of degrees of freedom and the number of continuity conditions, the mesh must be created with care. Due to the advantages from both an implementation perspective and potential good quality in the solution, it is nevertheless worthwhile to examine the properties of this approach. We present guidelines to ensure that the resulting conforming mesh is consistent with the O-method and also how to apply a reduced flux stencil for arbitrary polyhedral meshes.