2017/07/19 by Jérôme Droniou, Robert Eymard, Droniou, Jérôme +5 · 2 citations
Computer Science · Engineering · #65M06 #65M08 #65M12 #65M60 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1707.06034
openalex publication_date 2017/07/19 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
This article performs a unified convergence analysis of a variety of\nnumerical methods for a model of the miscible displacement of one\nincompressible fluid by another through a porous medium. The unified analysis\nis enabled through the framework of the gradient discretisation method for\ndiffusion operators on generic grids. We use it to establish a novel\nconvergence result in L^\∞(0,T; L2(\Ω)) of the approximate\nconcentration using minimal regularity assumptions on the solution to the\ncontinuous problem. The convection term in the concentration equation is\ndiscretised using a centred scheme. We present a variety of numerical tests\nfrom the literature, as well as a novel analytical test case. The performance\nof two schemes are compared on these tests; both are poor in the case of\nvariable viscosity, small diffusion and medium to small time steps. We show\nthat upstreaming is not a good option to recover stable and accurate solutions,\nand we propose a correction to recover stable and accurate schemes for all time\nsteps and all ranges of diffusion.\n