A stabilized difference scheme for deformable porous media and its numerical resolution by multigrid methods

This paper deals with the 2D system of incompressible poroelasticity equations in which an artificial stabilization term has been added to the discretization on collocated grids. Two issues are discussed: It is proved and shown that the additional term indeed brings stability and does not spoil the...

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Bibliographic Details
Published in:Computing and visualization in science 2008-03, Vol.11 (2), p.67-76
Main Authors: Gaspar, F. J., Lisbona, F. J., Oosterlee, C. W.
Format: Article
Language:English
Subjects:
Algorithms
Calculus of Variations and Optimal Control
Optimization
Computational Mathematics and Numerical Analysis
Computational techniques
Computer Applications in Chemistry
Convergence
Discrete systems
Exact sciences and technology
Formability
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical methods in physics
Mathematics
Mathematics and Statistics
Multigrid methods
Numerical Analysis
Physics
Poroelasticity
Porous media
Regular Article
Solid mechanics
Stability
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Visualization
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Summary:This paper deals with the 2D system of incompressible poroelasticity equations in which an artificial stabilization term has been added to the discretization on collocated grids. Two issues are discussed: It is proved and shown that the additional term indeed brings stability and does not spoil the second order accurate convergence. Secondly, various smoothers are examined in order to find an optimal multigrid method for the discrete system of equations. Numerical experiments confirm the stability and the second order accuracy, as well as fast multigrid convergence for a realistic poroelasticity experiment.
ISSN:1432-9360
1433-0369
DOI:10.1007/s00791-007-0061-1