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Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system

P. Luo, C. Rodrigo, F.J. Gaspar, C.W. Oosterlee
2018 Journal of Computational Physics  
The interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations.  ...  As a highly efficient solver for a saddle point system, the monolithic multigrid method is chosen in this paper.  ...  Conclusions In this paper, an efficient monolithic multigrid method is developed for a coupled system composed of a free fluid flow and a deformable porous medium.  ... 
doi:10.1016/ fatcat:7mdfsjttozfmrn5m45k553jjom

Poroelasticity problem: numerical difficulties and efficient multigrid solution

Carmen Rodrigo
2015 SeMA Journal  
On the other hand, a monolithic multigrid method is considered for the solution of the resulting system of equations after discretization by using the stabilized scheme.  ...  This multigrid method is designed with the help of an special local Fourier analysis that takes into account the specific characteristics of the considered block-relaxations.  ...  Introduction to poroelasticity problem Poroelasticity theory describes the interaction between the deformation of an elastic porous material and the fluid flow inside of it.  ... 
doi:10.1007/s40324-015-0054-9 fatcat:zmzurgqdbrewpikhj6oleztcxu

Reactive Flows in Deformable, Complex Media

Margot Gerritsen, Jan Martin Nordbotten, Iuliu Sorin Pop, Barbara Wohlmuth
2014 Oberwolfach Reports  
, and the key issue is to integrate the domain deformation in the multi-scale context.  ...  Many processes of highest actuality in the real life are described through systems of equations posed in complex domains.  ...  In regions involving deformable porous media the Darcy flow is coupled with elasticity and modeled by the Biot system of poroelasticity.  ... 
doi:10.4171/owr/2014/43 fatcat:cxkazxwlwnaqnmxamofkkhdnru

Meshless techniques for anisotropic diffusion

Annamaria Mazzia, Giorgio Pini, Flavio Sartoretto
2014 Applied Mathematics and Computation  
The latter would allow better use of parallel computers, since time-stepping is essentially a serial process. Moreover, it would be good for the methods to be of high order accuracy.  ...  A good numerical method would be locally mass conservative, produce no or minimal over/under-shoots, produce minimal numerical diffusion, and require no CFL time-step limit for stability.  ...  We show how to solve the equations using a global implicit approach in an efficient way, and we present the derived computational results.  ... 
doi:10.1016/j.amc.2014.03.032 fatcat:c527226gyfgbffnq4p67qxd7wi

Block-partitioned solvers for coupled poromechanics: A unified framework

Joshua A. White, Nicola Castelletto, Hamdi A. Tchelepi
2016 Computer Methods in Applied Mechanics and Engineering  
In the first approach, the system matrix is treated monolithically, and a Krylov iteration is used to update pressure and displacement unknowns simultaneously.  ...  These systems have an inherent block structure due to the coupled nature of the mass and momentum balance equations.  ...  This work was partially supported by the Petroleum Institute (PI) of Abu Dhabi and by the Reservoir Simulation Industrial Affiliates Consortium at Stanford University (SUPRI-B).  ... 
doi:10.1016/j.cma.2016.01.008 fatcat:lo5hlxr7sbdttaox7g2wyq27ba

Robust Block Preconditioners for Biot's Model [article]

James H. Adler and Francisco J. Gaspar and Xiaozhe Hu and Carmen Rodrigo and Ludmil T. Zikatanov
2017 arXiv   pre-print
The proposed block preconditioners are based on the well-posedness of the discrete linear systems.  ...  In this paper, we design robust and efficient block preconditioners for the two-field formulation of Biot's consolidation model, where stabilized finite-element discretizations are used.  ...  For the coupled poromechanics equations considered here, there are two typical approaches: fullycoupled or monolithic methods and iterative coupling methods.  ... 
arXiv:1705.08842v1 fatcat:w5amtcu2lvhnxcdxqc7lvi5cxq

Network-inspired versus Kozeny–Carman based permeability-porosity relations applied to Biot's poroelasticity model

Menel Rahrah, Luis A. Lopez-Peña, Fred Vermolen, Bernard Meulenbroek
2020 Journal of Mathematics in Industry  
Acknowledgements The authors acknowledge the financial support from the Netherlands Organisation for Scientific Research and the Mexican Institute of Petroleum. Funding The work of M.  ...  Rahrah was supported by the Netherlands Organisation for Scientific Research NWO (project number 13263). The work of L.A.  ...  Another approach that is widely used in coupling the flow and the mechanics in porous media is the fixed stress split method [10, 28] . Hong et al.  ... 
doi:10.1186/s13362-020-00087-z fatcat:ebmm5de55nagvcv4dshqnarix4

Computational Multiscale Solvers for Continuum Approaches

Francisco Montero-Chacón, José Sanz-Herrera, Manuel Doblaré
2019 Materials  
The availability and usefulness of this technique in the design of complex microstructural systems are highlighted along the text.  ...  Moreover, the predictable capability and potential of multiscale analysis may result in an interesting tool for the development of new concept materials, with desired macroscopic or apparent properties  ...  Acknowledgments: This work was carried out within the Virtual Materials Design project in Abengoa Research. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/ma12050691 pmid:30813637 pmcid:PMC6427293 fatcat:cnblwkmv6reibhxp4qtfefsgwi

Robust preconditioning for coupled Stokes–Darcy problems with the Darcy problem in primal form

Karl Erik Holter, Miroslav Kuchta, Kent-Andre Mardal
2020 Computers and Mathematics with Applications  
problem models porous fluid flow in a porous medium and its elastic deformation, with the two phenomena coupled together.  ...  Abstract The coupled Darcy-Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part.  ...  Robust preconditioning for coupled Stokes-Darcy problems with the Darcy problem in primal form Having discussed well-posedness of the Stokes and Darcy subproblems our main result concerning the coupled  ... 
doi:10.1016/j.camwa.2020.08.021 fatcat:3h7ziq6a5fcdxiszjuzyffdguu

Robust preconditioning of monolithically coupled multiphysics problems [article]

Karl Erik Holter, Miroslav Kuchta, Kent-Andre Mardal
2020 arXiv   pre-print
Furthermore, we show feasibility of the framework for two common multiphysics problems; namely the Darcy-Stokes problem and a fluid--structure interaction problem.  ...  In many applications, one wants to model physical systems consisting of two different physical processes in two different domains that are coupled across a common interface.  ...  Let Ω f and Ω p be the domain of the viscous flow and the porous medium, respectively, and Γ = ∂Ω f ∩ ∂Ω p be their common non-empty interface.  ... 
arXiv:2001.05527v1 fatcat:dugmaeyuuzawvgcx7xbtilm2xm

Numerical Stabilization of the Melt Front for Laser Beam Cutting [chapter]

Torsten Adolph, Willi Schönauer, Markus Niessen, Wolfgang Schulz
2010 Numerical Mathematics and Advanced Applications 2009  
The resulting linear systems are solved alternatively by the Multigrid method and Krylov subspace methods. We treat two types of boundary conditions: Dirichlet and natural boundary condition.  ...  The model is based on Navier-Stokes equations for viscous incompressible flow and convection-diffusion equation describing pollution transport.  ...  between the deformation of an elastic porous material and the fluid flow inside of it.  ... 
doi:10.1007/978-3-642-11795-4_6 fatcat:nx4nvuxaxfbcdjknopny53ck5e

Robust preconditioners for perturbed saddle-point problems and conservative discretizations of Biot's equations utilizing total pressure [article]

Wietse M. Boon, Miroslav Kuchta, Kent-Andre Mardal, Ricardo Ruiz-Baier
2020 arXiv   pre-print
We develop robust solvers for a class of perturbed saddle-point problems arising in the study of a second-order elliptic equation in mixed form (in terms of flux and potential), and of the four-field formulation  ...  of Biot's consolidation problem for linear poroelasticity (using displacement, filtration flux, total pressure and fluid pressure).  ...  We will here consider the equations of linear poroelasticity, where fluid flows in isothermal deformable porous media, assuming that the solid skeleton undergoes small strains.  ... 
arXiv:2011.05236v1 fatcat:j5burynnrja5dhcxw2dgdjf7ny

Influence of Foam Morphology on Flow and Heat Transport in a Random Packed Bed with Metallic Foam Pellets—An Investigation Using CFD

Ginu R. George, Marina Bockelmann, Leonhard Schmalhorst, Didier Beton, Alexandra Gerstle, Andreas Lindermeir, Gregor D. Wehinger
2022 Materials  
is used for the effective transport processes inside highly-porous foam pellets.  ...  Simulation inputs include the processing parameters relevant to Steam Methane Reforming (SMR), analyzed for low (Rep~100) and high (Rep~5000) flow regimes.  ...  Acknowledgments: We acknowledge support from the Open Access Publishing Fund of Clausthal University of Technology. Conflicts of Interest: The authors declare no conflict of interest. Appendix A  ... 
doi:10.3390/ma15113754 pmid:35683052 pmcid:PMC9181048 fatcat:64oyf44rjfdyrjuf73ifdvcloa

Bernaise: A flexible framework for simulating two-phase electrohydrodynamic flows in complex domains [article]

Gaute Linga, Asger Bolet, Joachim Mathiesen
2018 arXiv   pre-print
for electrostatics, the Cahn-Hilliard equation for the phase field (describing the interface separating the phases), and the Navier-Stokes equations for fluid flow.  ...  As an efficient alternative to solving the coupled system of partial differential equations in a monolithic manner, we present a linear, decoupled numerical scheme which sequentially solves the three sets  ...  It is known that electrohydrodynamic phenomena affects transport properties and energy dissipation in geological systems, as a fluid moving in a fluid-saturated porous medium sets up an electric field  ... 
arXiv:1805.11642v1 fatcat:fq3kc65u7reevj6e3y66uxvtre

Phase-field modeling of a fluid-driven fracture in a poroelastic medium

A. Mikelić, M. F. Wheeler, T. Wick
2015 Computational Geosciences  
The mathematical model consists of a linear elasticity system with fading elastic moduli as the crack grows, which is coupled with an elliptic variational inequality for the phase field variable and with  ...  Here we consider a fully coupled system where the pressure field is determined simultaneously with the displacement and the phase field.  ...  Introduction The coupling of flow and geomechanics in porous media is a major research topic in energy and environmental modeling.  ... 
doi:10.1007/s10596-015-9532-5 fatcat:yiwrmllh5rffze5o2kz5j3l6wy
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