On numerical solution of 1D poroelasticity equations in a multilayered domain

Abstract

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.

Straipsnyje pateikta Bioto sistemos poringai elastiškai terpei daugiasluosneje srityje diskretizacija baigtiniu tūriu metodu. Norint išvengti skaitinio sprendinio ne fiziniu osciliaciju atsirandančiu naudojant kolokacini tinkla, naudojamas judantis tinklas. Straipsnyje pateikti ivairūs skaitiniai eksperimentai iliustruoja baigtiniu skirtumu schemos tiksluma. Pirmoje tokio eksperimento dalyje sprendžiami uždaviniai, turintys analizinius sprendinius, ir analizuojama greičio, slegio, išstūmimo, itempiu artutiniu sprendiniu konvergavimo eile. Antroje eksperimento dalyje pateikta skaitinis realiu procesu modeliavimas.

Key words:

• poroelasticity
• multilayered material
• finite volume discretization
• MAC type grid