An optimization approach for flow simulations in poro-fractured media with complex geometries

Abstract

A new discretization approach is presented for the simulation of flow in complex poro-fractured media described by means of the Discrete Fracture and Matrix Model. The method is based on the numerical optimization of a properly defined cost-functional and allows to solve the problem without any constraint on mesh generation, thus overcoming one of the main complexities related to efficient and effective simulations in realistic DFMs.

3D-1D coupling on non conforming meshes via three-field optimization based domain decomposition

“…The advantages of the three-field based approach with respect to standard domain decomposition methods lie in the possibility of defining stable locally conservative numerical schemes on non conforming meshes [18]. Matching conditions at the interfaces are enforced by means of a PDE constrained numerical scheme, already proposed for simulation of the flow in poro-fractured media [19,20,21] and here proposed for 3D-1D coupling. The method is based on the minimization of a cost functional expressing the error in the fulfillment of interface conditions, constrained by constitutive laws on the various subdomains.…”

A gradient based resolution strategy for a PDE-constrained optimization approach for 3D-1D coupled problems

“…The present work is based on a re-formulation of the original 3D-3D problem into properly defined functional spaces, thus paving the way for a well posed formulation of the reduced 3D-1D problem [1]. The numerical resolution is further obtained through a PDE-constrained optimization based approach [17,18,19,20], in which problems in the 3D bulk domain and in the 1D inclusions are decoupled using a three-field based domain decomposition method. A cost functional, expressing the error in the fulfilment of interface conditions, is minimized to restore the coupling.…”