Constraint Preconditioning for the Coupled Stokes--Darcy System

Chidyagwai, Prince; Ladenheim, Scott; Szyld, Daniel B.

doi:10.1137/15m1032156

Cited by 36 publications

(31 citation statements)

References 34 publications

(52 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this context, preconditioned GMRES methods with block or constraint preconditioners [10,15,16] usually show a mesh-independent convergence Downloaded 12/19/17 to 131.211.208. 19.…”

Section: Multiblock Multigrid Algorithmmentioning

confidence: 99%

Uzawa Smoother in Multigrid for the Coupled Porous Medium and Stokes Flow System

Luo¹,

Rodrigo²,

Gaspar³

et al. 2017

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

Abstract. The multigrid solution of coupled porous media and Stokes flow problems is considered. The Darcy equation as the saturated porous medium model is coupled to the Stokes equations by means of appropriate interface conditions. We focus on an efficient multigrid solution technique for the coupled problem, which is discretized by finite volumes on staggered grids, giving rise to a saddle point linear system. Special treatment is required regarding the discretization at the interface. An Uzawa smoother is employed in multigrid, which is a decoupled procedure based on symmetric Gauss-Seidel smoothing for velocity components and a simple Richardson iteration for the pressure field. Since a relaxation parameter is part of a Richardson iteration, local Fourier analysis is applied to determine the optimal parameters. Highly satisfactory multigrid convergence is reported, and, moreover, the algorithm performs very well for small values of the hydraulic conductivity and fluid viscosity, which are relevant for applications.

show abstract

“…In this context, preconditioned GMRES methods with block or constraint preconditioners [10,15,16] usually show a mesh-independent convergence Downloaded 12/19/17 to 131.211.208. 19.…”

Section: Multiblock Multigrid Algorithmmentioning

confidence: 99%

Uzawa Smoother in Multigrid for the Coupled Porous Medium and Stokes Flow System

Luo¹,

Rodrigo²,

Gaspar³

et al. 2017

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

show abstract

“…The massive applications, such as karst aquifer subsurface flow system, interaction between the surface flows and subsurface flows, petroleum extraction, industrial filtration, biochemical transport, field flow fractionation for separation and characterization of proteins, blood flow in arteries and veins, etc, attract scientists and engineers to build related fluid dynamical models, including (Navier‐)Stokes‐Darcy model, Stokes‐Darcy‐transport model, Darcy‐Stokes‐Brinkman model, etc . It is not surprising that a great deal of effort has been devoted to develop appropriate numerical methods to solve the (Navier‐)Stokes‐Darcy fluid flow system, including coupled finite element methods, domain decomposition methods, Lagrange multiplier methods, mortar finite element methods, least‐square methods, partitioned time‐stepping methods, two‐grid and multigrid methods, discontinuous Galerkin finite element methods, boundary integral methods, and many others …”

Section: Introductionmentioning

confidence: 99%

Coupled and decoupled stabilized mixed finite element methods for nonstationary dual‐porosity‐Stokes fluid flow model

Mahbub

Nasu

et al. 2019

Numerical Meth Engineering

View full text Add to dashboard Cite

In this paper, we propose and analyze two stabilized mixed finite element methods for the dual-porosity-Stokes model, which couples the free flow region and microfracture-matrix system through four interface conditions on an interface. The first stabilized mixed finite element method is a coupled method in the traditional format. Based on the idea of partitioned time stepping, the four interface conditions, and the mass exchange terms in the dual-porosity model, the second stabilized mixed finite element method is decoupled in two levels and allows a noniterative splitting of the coupled problem into three subproblems. Due to their superior conservation properties and convenience of the computation of flux, mixed finite element methods have been widely developed for different types of subsurface flow problems in porous media. For the mixed finite element methods developed in this article, no Lagrange multiplier is used, but an interface stabilization term with a penalty parameter is added in the temporal discretization. This stabilization term ensures the numerical stability of both the coupled and decoupled schemes. The stability and the convergence analysis are carried out for both the coupled and decoupled schemes. Three numerical experiments are provided to demonstrate the accuracy, efficiency, and applicability of the proposed methods. KEYWORDS decoupled numerical methods, dual-porosity-Stokes model, horizontal wellbore, mixed finite elements, stabilization Int J Numer Methods Eng. 2019;120:803-833. wileyonlinelibrary.com/journal/nme 804 AL MAHBUB ET AL.model, It is not surprising that a great deal of effort has been devoted to develop appropriate numerical methods to solve the (Navier-)Stokes-Darcy fluid flow system, including coupled finite element methods, 17-21 domain decomposition methods, 22-31 Lagrange multiplier methods, 3,32,33 mortar finite element methods, 34,35 least-square methods, 36-38 partitioned time-stepping methods, 39,40 two-grid and multigrid methods, 41-44 discontinuous Galerkin finite element methods, 45-50 boundary integral methods, 51,52 and many others. [53][54][55][56][57][58] Although the traditional Stokes-Darcy model has been well studied, it has limitation to describe the heterogeneity of the porous medium which contains multiple porosities. It is worth to notice that the realistic naturally fractured reservoir consists of two coexisting and interacting medium, namely, tight matrix and microfractures. Furthermore, it is more important to characterize the intrinsic properties and accurately modeled the flow interactions between each medium. 59,60 The first multiporosity model was proposed by Barenblatt et al 61 for the naturally fractured reservoir in 1960 where the microfracture and matrix systems are formulated by individual but overlapping continua. Warren and Root 62 developed a homogeneous orthotropic dual-porosity model in 1963 based on the model proposed by Barenblatt. There are many applications for the dual-porosity model such as the geothermal system, hydrogeology, pe...

show abstract

“…For example, ILU factorizations have been extensively applied to PDE problems (see [329,330] for instance), and incomplete factorizations find considerable applicability as smoothers within multigrid [68]. Constraint preconditioners [278,[331][332][333] and augmented Lagrangian preconditioners [143,144,284,334] have also been widely used when solving PDEs. However, it can also be that the nature of PDE and optimization problems are distinct, and so one must carefully tailor preconditioned iterative solvers to the problem at hand.…”

Section: Link To Pdes and Pde-constrained Optimizationmentioning

confidence: 99%

Section: Preconditioners For Optimization Problemsmentioning

confidence: 99%

Preconditioners for Krylov subspace methods: An overview

Pearson

Pestana

2020

GAMM-Mitteilungen

View full text Add to dashboard Cite

When simulating a mechanism from science or engineering, or an industrial process, one is frequently required to construct a mathematical model, and then resolve this model numerically. If accurate numerical solutions are necessary or desirable, this can involve solving large-scale systems of equations. One major class of solution methods is that of preconditioned iterative methods, involving preconditioners which are computationally cheap to apply while also capturing information contained in the linear system. In this article, we give a short survey of the field of preconditioning. We introduce a range of preconditioners for partial differential equations, followed by optimization problems, before discussing preconditioners constructed with less standard objectives in mind.

show abstract

Constraint Preconditioning for the Coupled Stokes--Darcy System

Cited by 36 publications

References 34 publications

Uzawa Smoother in Multigrid for the Coupled Porous Medium and Stokes Flow System

Uzawa Smoother in Multigrid for the Coupled Porous Medium and Stokes Flow System

Coupled and decoupled stabilized mixed finite element methods for nonstationary dual‐porosity‐Stokes fluid flow model

Preconditioners for Krylov subspace methods: An overview

Contact Info

Product

Resources

About