Flow in fractured porous media occurs in the earth's subsurface, in biological tissues, and in man-made materials. Fractures have a dominating influence on flow processes, and the last decade has seen an extensive development of models and numerical methods that explicitly account for their presence. To support these developments, four benchmark cases for single-phase flow in three-dimensional fractured porous media are presented. The cases are specifically designed to test the methods' capabilities in handling various complexities common to the geometrical structures of fracture networks. Based on an open call for participation, results obtained with 17 numerical methods were collected. This paper presents the underlying mathematical model, an overview of the features of the participating numerical methods, and their performance in solving the benchmark cases.
This work presents a modeling approach for single-phase flow in 3D fractured porous media with non-conforming meshes. To this end, a Lagrange multiplier method is combined with a parallel L 2 -projection variational transfer approach. This Lagrange multiplier method enables the use of non-conforming meshes and depicts the variable coupling between fracture and matrix domain. The L 2 -projection variational transfer allows general, accurate, and parallel projection of variables between non-conforming meshes (i.e. between fracture and matrix domain). Comparisons of simulations with 2D benchmarks show good agreement, and the method is further validated on 3D fracture networks by comparing it to results from conforming mesh simulations which were used as a reference. Application to realistic fracture networks with hundreds of fractures is demonstrated. Mesh size and mesh convergence are investigated for benchmark cases and 3D fracture network applications. Results demonstrate that the Lagrange multiplier method, in combination with the L 2 -projection method, is capable of modeling single-phase flow through realistic 3D fracture networks.
We provide a computational comparison of the performance of stentless and stented aortic prostheses, in terms of aortic root displacements and internal stresses. To this aim, we consider three real patients; for each of them, we draw the two prostheses configurations, which are characterized by different mechanical properties and we also consider the native configuration. For each of these scenarios, we solve the fluid-structure interaction problem arising between blood and aortic root, through Finite Elements. In particular, the Arbitrary Lagrangian-Eulerian formulation is used for the numerical solution of the fluid-dynamic equations and a hyperelastic material model is adopted to predict the mechanical response of the aortic wall and the two prostheses. The computational results are analyzed in terms of aortic flow, internal wall stresses and aortic wall/prosthesis displacements; a quantitative comparison of the mechanical behavior of the three scenarios is reported. The numerical results highlight a good agreement between stentless and native displacements and internal wall stresses, whereas higher/non-physiological stresses are found for the stented case.
Hydro-mechanical processes in rough fractures are highly non-linear and govern productivity and associated risks in a wide range of reservoir engineering problems. To enable high-resolution simulations of hydro-mechanical processes in fractures, we present an adaptation of an immersed boundary method to compute fluid flow between rough fracture surfaces. The solid domain is immersed into the fluid domain and both domains are coupled by means of variational volumetric transfer operators. The transfer operators implicitly resolve the boundary between the solid and the fluid, which simplifies the setup of fracture simulations with complex surfaces. It is possible to choose different formulations and discretization schemes for each subproblem and it is not necessary to remesh the fluid grid. We use benchmark problems and real fracture geometries to demonstrate the following capabilities of the presented approach: (1) Resolving the boundary of the rough 1 arXiv:1812.08572v2 [physics.geo-ph] 8 Aug 2019 fracture surface in the fluid; (2) Capturing fluid flow field changes in a fracture which closes under increasing normal load; and (3) Simulating the opening of a fracture due to increased fluid pressure.
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