2017/06/08 by Hanz Martin Cheng, Jérôme Droniou, Cheng, Hanz Martin +1
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1706.02452
openalex publication_date 2017/06/08 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
We design a numerical approximation of a system of partial differential\nequations modelling the miscible displacement of a fluid by another in a porous\nmedium. The advective part of the system is discretised using a characteristic\nmethod, and the diffusive parts by a finite volume method. The scheme is\napplicable on generic (possibly non-conforming) meshes as encountered in\napplications. The main features of our work are the reconstruction of a Darcy\nvelocity, from the discrete pressure fluxes, that enjoys a local consistency\nproperty, an analysis of implementation issues faced when tracking, via the\ncharacteristic method, distorted cells, and a new treatment of cells near the\ninjection well that accounts better for the conservativity of the injected\nfluid.\n