×

zbMATH — the first resource for mathematics

A LATIN computational strategy for multiphysics problems: application to poroelasticity. (English) Zbl 1106.74425
Summary: Multiphysics phenomena and coupled-field problems usually lead to analyses which are computationally intensive. Strategies to keep the cost of these problems affordable are of special interest. For coupled fluid-structure problems, for instance, partitioned procedures and staggered algorithms are often preferred to direct analysis. In this paper, we describe a new strategy for solving coupled multiphysics problems which is built upon the LArge Time INcrement (LATIN) method. The proposed application concerns the consolidation of saturated porous soil, which is a strongly coupled fluid-solid problem. The goal of this paper is to discuss the efficiency of the proposed approach, especially when using an appropriate time-space approximation of the unknowns for the iterative resolution of the uncoupled global problem. The use of a set of radial loads as an adaptive approximation of the solution during iterations will be validated and a strategy for limiting the number of global resolutions will be tested on multiphysics problems.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Felippa, Staggered transient analysis procedures for coupled mechanical systems: formulation, Computer Methods in Applied Mechanics and Engineering 24 pp 61– (1980) · Zbl 0453.73091 · doi:10.1016/0045-7825(80)90040-7
[2] Felippa, Partitioned analysis for coupled mechanical systems, Engineering Computations 5 pp 123– (1988)
[3] Lewis, Coupling versus uncoupling in soil consolidation, International Journal for Numerical and Analytical Methods in Geomechanics 15 pp 533– (1991)
[4] Ohayor, Fluid-Structure Interaction: Applied Numerical Methods (1995)
[5] Piperno, Partitioned procedures for the transient solution of coupled aeroelastic problems. Part I: model problem, theory and two-dimensional application, Computer Methods in Applied Mechanics and Engineering 124 pp 79– (1995) · Zbl 1067.74521 · doi:10.1016/0045-7825(95)92707-9
[6] Schrefler, The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media (1998) · Zbl 0935.74004
[7] Farhat, Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems, Computer Methods in Applied Mechanics and Engineering 182 pp 499– (2000) · Zbl 0991.74069 · doi:10.1016/S0045-7825(99)00206-6
[8] Dureisseix, Contemporary Mathematics, Domain Decomposition Methods 10 218 pp 246– (1998)
[9] Ladevèze, A micro/macro approach for parallel computing of heterogeneous structures, International Journal for Computational Civil and Structural Engineering 1 pp 18– (2000)
[10] Ladevèze, Nonlinear Computational Structural Mechanics-New Approaches and Non-Incremental Methods of Calculation (1999) · Zbl 0912.73003
[11] Ladevèze, Sur une famille d’algorithmes en mécanique des structures, Comptes Rendus de l’Académie des Sciences, Series IIB 300 pp 41– (1985) · Zbl 0597.73089
[12] Dureisseix, Proceedings of the First M.I.T. Conference on Computational Fluid and Solid Mechanics pp 1143– (2001)
[13] Dureisseix D Ladevèze P Schrefler BA LATIN computational strategy for multiphysics problems 2001
[14] Coussy, Mechanics of porous continua (1995)
[15] GRECO 1990
[16] Zienkiewicz, The patch test for mixed formulations, International Journal for Numerical Methods in Engineering 23 pp 1873– (1986) · Zbl 0614.65115
[17] Brezzi, Mixed and Hybrid Finite Element Methods, Computational Mathematics 15 (1991) · Zbl 0788.73002
[18] Zienkiewicz, The Finite Element Method (2000) · Zbl 0962.76056
[19] Matteazzi, Advances in Computational Structures Technology, in: Comparisons of partitioned solution procedures for transient coupled problems in sequential and parallel processing pp 351– (1996)
[20] Turska, On convergence conditions of partitioned solution procedures for consolidation problems, Computer Methods in Applied Mechanics and Engineering 106 pp 51– (1993) · Zbl 0783.76064 · doi:10.1016/0045-7825(93)90184-Y
[21] Park, Stabilization of partitioned solution procedure for pore fluid-soil interaction analysis, International Journal for Numerical Methods in Engineering 19 pp 1669– (1983) · Zbl 0519.76095
[22] Zienkiewicz, Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems, International Journal for Numerical Methods in Engineering 26 pp 1039– (1988) · Zbl 0634.73110
[23] Saetta, Unconditionally convergent partitioned solution procedure for dynamic coupled mechanical systems, International Journal for Numerical Methods in Engineering 33 pp 1975– (1992) · Zbl 0775.73345
[24] Barrett, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (1994)
[25] Verpeaux, Calcul des Structures et Intelligence Artificielle 2 pp 261– (1998)
[26] Saad, Iterative Methods for Sparse Linear Systems (1996) · Zbl 1031.65047
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.