Analysis of Partitioned Methods for the Biot System

Bukac, Martina; Layton, William; Moraiti, Marina; Tran, Hoang A.; Trenchea, Catalin S.

doi:10.1002/num.21968

Title: Analysis of Partitioned Methods for the Biot System

Journal Article · Wed Feb 18 00:00:00 EST 2015 · Numerical Methods for Partial Differential Equations

DOI:https://doi.org/10.1002/num.21968· OSTI ID:1335329

Bukac, Martina ^[1]; Layton, William ^[2]; Moraiti, Marina ^[2]; Tran, Hoang A. ^[3]; Trenchea, Catalin S. ^[3]

Univ. of Notre Dame, IN (United States)
Univ. of Pittsburgh, PA (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

In this work, we present a comprehensive study of several partitioned methods for the coupling of flow and mechanics. We derive energy estimates for each method for the fully-discrete problem. We write the obtained stability conditions in terms of a key control parameter defined as a ratio of the coupling strength and the speed of propagation. Depending on the parameters in the problem, give the choice of the partitioned method which allows the largest time step. (C) 2015 Wiley Periodicals, Inc.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1335329

Journal Information:: Numerical Methods for Partial Differential Equations, Vol. 31, Issue 6; ISSN 0749-159X

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 9 works

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References (17)

Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems Zienkiewicz, O. C.; Paul, D. K.; Chan, A. H. C. International Journal for Numerical Methods in Engineering, Vol. 26, Issue 5 https://doi.org/10.1002/nme.1620260504	journal	May 1988
A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems Armero, F.; Simo, J. C. International Journal for Numerical Methods in Engineering, Vol. 35, Issue 4 https://doi.org/10.1002/nme.1620350408	journal	September 1992
A priori stability estimates and unconditionally stable product formula algorithms for nonlinear coupled thermoplasticity Armero, F.; Simo, J. C. International Journal of Plasticity, Vol. 9, Issue 6 https://doi.org/10.1016/0749-6419(93)90036-P	journal	January 1993
Formulation and finite element implementation of a multiplicative model of coupled poro-plasticity at finite strains under fully saturated conditions Armero, F. Computer Methods in Applied Mechanics and Engineering, Vol. 171, Issue 3-4 https://doi.org/10.1016/S0045-7825(98)00211-4	journal	April 1999
Stability and convergence of sequential methods for coupled flow and geomechanics: Drained and undrained splits Kim, J.; Tchelepi, H. A.; Juanes, R. Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 23-24 https://doi.org/10.1016/j.cma.2011.02.011	journal	June 2011
Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits Kim, J.; Tchelepi, H. A.; Juanes, R. Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 13-16 https://doi.org/10.1016/j.cma.2010.12.022	journal	March 2011
Convergence of iterative coupling for coupled flow and geomechanics Mikelić, Andro; Wheeler, Mary F. Computational Geosciences, Vol. 17, Issue 3 https://doi.org/10.1007/s10596-012-9318-y	journal	October 2012
Modeling Groundwater Flow and Contaminant Transport Bear, Jacob; Cheng, Alexander H. -D. https://doi.org/10.1007/978-1-4020-6682-5	book	January 2010
Decoupled schemes for a non-stationary mixed Stokes-Darcy model Mu, Mo; Zhu, Xiaohong Mathematics of Computation, Vol. 79, Issue 270 https://doi.org/10.1090/S0025-5718-09-02302-3	journal	September 2009
Partitioned Time Stepping Method for Fully Evolutionary Stokes--Darcy Flow with Beavers--Joseph Interface Conditions Shan, Li; Zheng, Haibiao SIAM Journal on Numerical Analysis, Vol. 51, Issue 2 https://doi.org/10.1137/110828095	journal	January 2013
A decoupling method with different subdomain time steps for the nonstationary stokes-darcy model Shan, Li; Zheng, Haibiao; Layton, William J. Numerical Methods for Partial Differential Equations, Vol. 29, Issue 2 https://doi.org/10.1002/num.21720	journal	April 2012
Partitioned time discretization for parallel solution of coupled ODE systems Connors, Jeffrey M.; Miloua, Attou BIT Numerical Mathematics, Vol. 51, Issue 2 https://doi.org/10.1007/s10543-010-0295-z	journal	November 2010
Analysis of Long Time Stability and Errors of Two Partitioned Methods for Uncoupling Evolutionary Groundwater--Surface Water Flows Layton, William; Tran, Hoang; Trenchea, Catalin SIAM Journal on Numerical Analysis, Vol. 51, Issue 1 https://doi.org/10.1137/110834494	journal	January 2013
Accurate, stable and efficient Navier–Stokes solvers based on explicit treatment of the pressure term Johnston, Hans; Liu, Jian-Guo Journal of Computational Physics, Vol. 199, Issue 1 https://doi.org/10.1016/j.jcp.2004.02.009	journal	September 2004
Uncoupling evolutionary groundwater-surface water flows using the Crank-Nicolson Leapfrog method: Uncoupling Evolutionary Groundwater Surface Water Flows Kubacki, Michaela Numerical Methods for Partial Differential Equations, Vol. 29, Issue 4 https://doi.org/10.1002/num.21751	journal	November 2012
Stability of two IMEX methods, CNLF and BDF2-AB2, for uncoupling systems of evolution equations Layton, W.; Trenchea, C. Applied Numerical Mathematics, Vol. 62, Issue 2 https://doi.org/10.1016/j.apnum.2011.10.006	journal	February 2012
Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity Wheeler, Mary; Xue, Guangri; Yotov, Ivan Computational Geosciences, Vol. 18, Issue 1 https://doi.org/10.1007/s10596-013-9382-y	journal	November 2013

Cited By (3)

Second‐order time discretization for a coupled quasi‐Newtonian fluid‐poroelastic system Kunwar, Hemanta; Lee, Hyesuk; Seelman, Kyle International Journal for Numerical Methods in Fluids, Vol. 92, Issue 7 https://doi.org/10.1002/fld.4801	journal	December 2019
A second‐order partitioned method with different subdomain time steps for the evolutionary Stokes‐Darcy system Li, Yi; Hou, Yanren Mathematical Methods in the Applied Sciences, Vol. 41, Issue 5 https://doi.org/10.1002/mma.4744	journal	January 2018
Numerical analysis of the coupling of free fluid with a poroelastic material Cesmelioglu, Aycil; Chidyagwai, Prince Numerical Methods for Partial Differential Equations, Vol. 36, Issue 3 https://doi.org/10.1002/num.22437	journal	November 2019

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97 MATHEMATICS AND COMPUTING
Biot system
partitioned methods
poroelasticity
STOKES-DARCY MODEL
STABILITY
EXPLICIT
FLOW

Title: Analysis of Partitioned Methods for the Biot System

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