Numerical Solution of Plate Poroelasticity Problems

被引：0
作者：
O. P. Iliev
A. E. Kolesov
P. N. Vabishchevich
机构：
[1] Fraunhofer Institute for Industrial Mathematics,
[2] North-Eastern Federal University,undefined
[3] Nuclear Safety Institute,undefined
[4] RAS,undefined
来源：
Transport in Porous Media | 2016年 / 115卷
关键词：
Poroelasticity; Operator-difference schemes; Splitting scheme; Regularization; 34Q74; 65M12; 65M60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider the numerical solution of boundary value problems for poroelastic plates. The basic system of equations consists of the biharmonic equation for vertical displacement and nonstationary equation for pressure in the porous medium. The computational algorithm is based on the finite element approximation in longitudinal coordinates and the finite-difference approximation in time. We formulate standard stability conditions for two-level schemes with weights. The computational implementation of such schemes is based on solving a system of coupled equations: fourth-order elliptic equation for displacement and second-order elliptic equation for pressure. We construct unconditionally stable splitting schemes with respect to physical processes, when the transition to a new time level is associated with solving separate problems for the desired displacement and pressure.
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页码：563 / 580
页数：17
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