2019/06/13 by Elyes Ahmed, Ahmed, Elyes, Alessio Fumagalli +9
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1906.05831
openalex publication_date 2019/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we consider compressible single-phase flow problems in a porous\nmedia containing a fracture. In the latter, a non-linear pressure-velocity\nrelation is prescribed. Using a non-overlapping domain decomposition procedure,\nwe reformulate the global problem into a non-linear interface problem. We then\nintroduce two new algorithms that are able to efficiently handle the\nnon-linearity and the coupling between the fracture and the matrix, both based\non linearization by the so-called L-scheme. The first algorithm, named MoLDD,\nuses the L-scheme to resolve the non-linearity, requiring at each iteration to\nsolve the dimensional coupling via a domain decomposition approach. The second\nalgorithm, called ItLDD, uses a sequential approach in which the dimensional\ncoupling is part of the linearization iterations. For both algorithms, the\ncomputations are reduced only to the fracture by pre-computing, in an offline\nphase, a multiscale flux basis (the linear Robin-to-Neumann co-dimensional\nmap), that represent the flux exchange between the fracture and the matrix. We\npresent extensive theoretical findings and in particular, the stability and the\nconvergence of both schemes are obtained, where user given parameters are\noptimized to minimise the number of iterations. Examples on two important\nfracture models are computed with the library PorePy and agree with the\ndeveloped theory.\n