Finite-difference analysis of fully dynamic problems for saturated porous media |
| |
Authors: | N Boal FJ GasparFJ Lisbona PN Vabishchevich |
| |
Institution: | a Department of Applied Mathematics, University of Zaragoza, María de Luna 3, 50018, Zaragoza, Spainb Department of Applied Mathematics, University of Zaragoza, Pedro Cerbuna 12, 50009, Zaragoza, Spainc Keldysh Institute of Applied Mathematics, 4-A. Miusskaya Sq. 125047 Moscow, Russia |
| |
Abstract: | Finite-difference methods, using staggered grids in space, are considered for the numerical approximation of fully dynamic poroelasticity problems. First, a family of second-order schemes in time is analyzed. A priori estimates for displacements in discrete energy norms are obtained and the corresponding convergence results are proved. Numerical examples are given to illustrate the convergence properties of these methods. As in the case of an incompressible fluid and small permeability, these schemes suffer from spurious oscillations in time, a first order scheme is proposed and analyzed. For this new scheme a priori estimates and convergence results are also given. Finally, numerical examples in one and two dimensions are presented to show the good monotonicity properties of this method. |
| |
Keywords: | Poroelasticity Finite-differences Staggered grids Three-level schemes |
本文献已被 ScienceDirect 等数据库收录! |
|