# A Parameter-Robust Iterative Method for Stokes-Darcy Problems Retaining Local Mass Conservation

@article{Boon2020API, title={A Parameter-Robust Iterative Method for Stokes-Darcy Problems Retaining Local Mass Conservation}, author={Wietse M. Boon}, journal={ArXiv}, year={2020}, volume={abs/2209.13421} }

We consider a coupled model of free-flow and porous medium flow, governed by stationary Stokes and Darcy flow, respectively. The coupling between the two systems is enforced by introducing a single variable representing the normal flux across the interface. The problem is reduced to a system concerning only the interface flux variable, which is shown to be well-posed in appropriately weighted norms. An iterative solution scheme is then proposed to solve the reduced problem such that mass is…

## 4 Citations

### Robust monolithic solvers for the Stokes-Darcy problem with the Darcy equation in primal form

- Computer ScienceSIAM Journal on Scientific Computing
- 2022

This work constructs mesh-independent and parameter-robust monolithic solvers for the coupled primal Stokes-Darcy problem and suggests robust preconditioners that utilize operators in fractional Sobolev spaces.

### Flux-mortar mixed finite element methods with multipoint flux approximation

- EngineeringComputer Methods in Applied Mechanics and Engineering
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### Domain decomposition solvers for operators with fractional interface perturbations

- Computer ScienceArXiv
- 2022

Efficient and parameter-robust algorithms for interfaceperturbed operators based on the non-overlapping domain decomposition method for preconditioning of interface-coupled multiphysics systems are developed.

### Flux-mortar mixed finite element methods on non-matching grids

- MathematicsSIAM J. Numer. Anal.
- 2022

A mortar technique for mixed finite element approximations of Darcy flow on non-matching grids in which the normal flux is chosen as the coupling variable is investigated, showing that the same domain decomposition technique is applicable to a class of saddle point problems satisfying mild assumptions.

## References

SHOWING 1-10 OF 39 REFERENCES

### Analysis of fully-mixed finite element methods for the Stokes-Darcy coupled problem

- MathematicsMath. Comput.
- 2011

This paper analyzes fully-mixed finite element methods for the coupling of fluid flow with porous media flow and shows that with the present approach the Stokes and Darcy flows can be approximated with the same family of finite element subspaces without adding any stabilization term.

### Unified finite element discretizations of coupled Darcy–Stokes flow

- Computer Science
- 2009

Some new finite element methods for flows which are governed by the linear stationary Stokes system on one part of the domain and by a second order elliptic equation derived from Darcy's law in the rest of thedomain are discussed.

### Robin-Robin Domain Decomposition Methods for the Stokes-Darcy Coupling

- Computer Science, MathematicsSIAM J. Numer. Anal.
- 2007

The convergence of some iteration-by-subdomain methods based on Robin conditions on the interface are proved, and for suitable finite element approximations it is shown that the rate of convergence is independent of the mesh size.

### Coupling staggered-grid and MPFA finite volume methods for free flow/porous-medium flow problems

- PhysicsJ. Comput. Phys.
- 2020

### Domain decomposition methods for the coupling of surface and groundwater flows

- Mathematics
- 2004

The purpose of this thesis is to investigate, from both the mathematical and numerical viewpoint, the coupling of surface and porous media flows, with particular concern on environmental…

### Balancing Domain Decomposition Methods for Mortar Coupling Stokes-Darcy Systems

- Computer Science
- 2007

This work considers Stokes equations in the fluid region Ωf and Darcy equations for the filtration velocity in the porous medium Ωp, and coupled at the interface Γ with adequate transmission conditions, and proposes two preconditioners based on balancing domain decomposition methods.

### Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems

- PhysicsComputational Geosciences
- 2015

A model formulation to describe fluid flows in coupled saturated/unsaturated porous medium and adjacent free flow regions is proposed. The Stokes equations are applied in the free flow domain, while…

### On the Derivation of Optimized Transmission Conditions for the Stokes-Darcy Coupling

- Computer Science
- 2020

This manuscript studies OSM as an iterative method and as a preconditioner for GMRES and shows that the discrepancy is not due to the Krylov acceleration but to a limitation in the derived convergence factor.

### On the Conditions for Coupling Free Flow and Porous-Medium Flow in a Finite Volume Framework

- Physics
- 2017

This article presents model concepts for the coupling of one-phase compositional non-isothermal Navier-Stokes flow to two-phase compositional non-isothermal Darcy flow in a finite volume framework.…

### Robust Discretization of Flow in Fractured Porous Media

- Computer ScienceSIAM J. Numer. Anal.
- 2018

This formulation is novel in that it employs the normal fluxes as the mortar variable within the mixed finite element framework, resulting in a formulation that couples the flow in the fractures with the surrounding domain with a strong notion of mass conservation.