Scalable algorithms for three-field mixed finite element coupled poromechanics

Castelletto, Nicola; White, Joshua A.; Ferronato, Massimiliano

doi:10.1016/j.jcp.2016.09.063

Cited by 71 publications

(69 citation statements)

References 67 publications

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“…A. This approach has been demonstrated efficient for coupled poromechanical problems (see, e.g., Castelletto et al, 2016;Ferronato et al, 2010). Here we apply it to the rupture problem.…”

Section: Preconditioner Designmentioning

confidence: 99%

Fully Dynamic Spontaneous Rupture Due to Quasi‐Static Pore Pressure and Poroelastic Effects: An Implicit Nonlinear Computational Model of Fluid‐Induced Seismic Events

Jin

Zoback

2018

JGR Solid Earth

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Fluid perturbations play a pivotal role in triggering earthquakes. However, the role of fluid in the coseismic rupture process remains largely unknown. To this end, we develop a 2‐D fully dynamic spontaneous rupture model for fluid‐induced earthquakes. The effect of fluid in the preseismic quasi‐static regime is modeled as either pore pressure diffusion or fully coupled poroelasticity, using our Jin and Zoback (2017, https://doi.org/10.1002/2017JB014892) computational model. The two approaches lead to radically different predictions on the time of earthquake nucleation. Correspondingly, the evolved fluid pressure or poroelastic stress on the fault, together with the spatially altered density of the fluid‐saturated hosting rock, is passed to the dynamic regime. Under the assumption of an undrained coseismic fluid‐solid system, we discretize the fully dynamic Cauchy equation of motion subjected to an exact fault contact constraint using a split‐node finite element method in space and an implicit Newmark family finite difference method in time. Within each time step, a fully implicit Newton‐Raphson scheme is implemented iteratively for linearizing the fully discrete equations. Within each Newton iteration, a physics‐based and nonstationary preconditioner is designed to accelerate the convergence of the selected generalized minimal residual method iterative linear solver. The effect of fluid is highlighted throughout the discretization and computational procedures. Finally, by conducting a numerical experiment, we illustrate that a fully coupled poroelastic model can lead to significantly different predictions on coseismic rupture behaviors and wavefields compared to a decoupled model. Our computational model can also serve as one of the earliest full‐physics modeling tool for fluid‐induced earthquakes.

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“…A. This approach has been demonstrated efficient for coupled poromechanical problems (see, e.g., Castelletto et al, 2016;Ferronato et al, 2010). Here we apply it to the rupture problem.…”

Section: Preconditioner Designmentioning

confidence: 99%

Fully Dynamic Spontaneous Rupture Due to Quasi‐Static Pore Pressure and Poroelastic Effects: An Implicit Nonlinear Computational Model of Fluid‐Induced Seismic Events

Jin

Zoback

2018

JGR Solid Earth

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“…By doing so, displacements, Darcy's velocity, and pore pressure may be discretized using linear triangles, lowest order Raviart-Thomas, and piece-wise constant shape functions, respectively, which allows for element-wise mass conservation. 31,32 In the undrained limit, this element is unstable and exhibit pore pressure oscillations, that might be solved by employing a quadratic discretization for the skeleton displacement. 33 After obtaining the weak form of the balance equations, Equations 15, 16, and 17, the semidiscrete equations of the hydromechanical formulation are obtained.…”

Section: Weak Form and Spatial Discretizationmentioning

confidence: 99%

“…k + 1 indicates the current step. An implicit monolithic solver is used for time integration of Equation 32. According to Wriggers, 35 time integration schemes may be generally written in terms of the incremental displacements, ie,…”

Section: Time Integration Schemementioning

confidence: 99%

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Low‐order stabilized finite element for the full Biot formulation in soil mechanics at finite strain

Monforte

Navas

Carbonell

et al. 2019

Num Anal Meth Geomechanics

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“…It is analyzed that a fully-implicit method outper-40 forms the convergence rate of the sequential-implicit methods. Following this approach a family of preconditioners to accelerate the convergence of Krylov subspace methods has been recently proposed for the three-field formulation of the poromechanics problem [14].…”

Section: Introductionmentioning

confidence: 99%

On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics

Gaspar

Rodrigo

2017

Computer Methods in Applied Mechanics and Engineering

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Please cite this article as: F.J. Gaspar, C. Rodrigo, On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics, Comput. Methods Appl. Mech. Engrg. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics This solver combines the advantages of being a fully coupled method, with the benefit of decoupling the flow and the mechanics part in the smoothing algorithm. Moreover, the fixed-stress split smoother is based on the physics of the problem, and therefore all parameters involved in the relaxation are based on the physical properties of the medium and are given a priori. A local Fourier analysis is applied to study the convergence of the multigrid method and to support the good convergence results obtained. The proposed geometric multigrid algorithm is used to solve several tests in semi-structured triangular grids, in order to show the good behaviour of the method and its practical utility.

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Scalable algorithms for three-field mixed finite element coupled poromechanics

Cited by 71 publications

References 67 publications

Fully Dynamic Spontaneous Rupture Due to Quasi‐Static Pore Pressure and Poroelastic Effects: An Implicit Nonlinear Computational Model of Fluid‐Induced Seismic Events

Fully Dynamic Spontaneous Rupture Due to Quasi‐Static Pore Pressure and Poroelastic Effects: An Implicit Nonlinear Computational Model of Fluid‐Induced Seismic Events

Low‐order stabilized finite element for the full Biot formulation in soil mechanics at finite strain

On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics

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