Finite volume discretization of Biot system of poroelasticity in a multilayered domain is presented. Staggered grid is used in order to avoid non‐physical oscillations of the numerical solution, appearing when a collocated grid is used. Various numerical experiments are presented in order to illustrate the accuracy of the finite difference scheme. In the first group of experiments, problems having analytical solutions are solved, and the order of convergence for the velocity, the pressure, the displacements, and the stresses is analyzed. In the second group of experiments numerical solution of real problems is presented.
Skaitinis vienmačių lygčių poringai elastiškai terpei sprendimas daugiasluosnėje srityje
Straipsnyje pateikta Bioto sistemos poringai elastiškai terpei daugiasluoksnėje srityje diskretizacija baigtinių tūrių metodu. Norint išvengti skaitinio sprendinio ne fizinių osciliacijų atsirandančių naudojant kolokacinį tinklą, naudojamas judantis tinklas. Straipsnyje pateikti įvairūs skaitiniai eksperimentai iliustruoja baigtinių skirtumu schemos tikslumą. Pirmoje tokio eksperimento dalyje sprendžiami uždaviniai, turintys analizinius sprendinius, ir analizuojama greičio, slėgio, išstūmimo, įtempių artutinių sprendinių konvergavimo eilė. Antroje eksperimento dalyje pateikta skaitinis realių procesų modeliavimas.
Naumovich, A., Iliev, O., Gaspar, F., Lisbona, F., & Vabishchevich, P. (2005). On numerical solution of 1D poroelasticity equations in a multilayered domain. Mathematical Modelling and Analysis, 10(3), 287-304. https://doi.org/10.3846/13926292.2005.9637288
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