Navier-Stokes/Darcy Coupling: Modeling, Analysis, and Numerical Approximation
TLDR
In this article, an overview of known and new results about the coupling of Navier-Stokes and Darcy equations to model the filtration of incompressible fluids through porous media is presented.Citations
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Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction
TL;DR: In this paper, residual-based stabilization techniques for the Biot system were designed for the Navier-Stokes/Biot system, motivated by the variational multiscale approach.
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Numerical analysis of the Navier–Stokes/Darcy coupling
TL;DR: This work proposes and analyzes iterative methods to solve a conforming finite element approximation of the coupled problem of the Navier–Stokes and Darcy equations.
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Analysis of Long Time Stability and Errors of Two Partitioned Methods for Uncoupling Evolutionary Groundwater--Surface Water Flows
TL;DR: This report analyzes and tests two partitioned (noniterative, domain decomposition) methods for the fully evolutionary Stokes--Darcy problem and proves unconditional, long time (over $0\leq t<\infty $) stability of both partitioned methods.
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A decoupling method with different subdomain time steps for the nonstationary stokes–darcy model
TL;DR: A multirate, decoupling algorithm, which allows different time steps in the fluid region and the porous region for the nonstationary Stokes–Darcy problem, is analyzed.
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A Domain Decomposition Method for the Steady-State Navier-Stokes-Darcy Model with Beavers-Joseph Interface Condition
TL;DR: A Robin-type multiphysics domain decomposition method (DDM) for the steady-state Navier--Stokes--Darcy model with three interface conditions with well-posedness is proposed and analyzed by using a branch of nonsingular solutions.
References
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Book
Iterative Methods for Sparse Linear Systems
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
Journal ArticleDOI
General Theory of Three‐Dimensional Consolidation
TL;DR: In this article, the number of physical constants necessary to determine the properties of the soil is derived along with the general equations for the prediction of settlements and stresses in three-dimensional problems.
Book
Finite Element Method for Elliptic Problems
TL;DR: In this article, Ciarlet presents a self-contained book on finite element methods for analysis and functional analysis, particularly Hilbert spaces, Sobolev spaces, and differential calculus in normed vector spaces.
Book
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
TL;DR: This paper presents the results of an analysis of the "Stream Function-Vorticity-Pressure" Method for the Stokes Problem in Two Dimensions and its applications to Mixed Approximation and Homogeneous Stokes Equations.