arXiv subjects

Paula Strohbeck

Publications and source records attributed to Paula Strohbeck.

3 recordsLinked to original sources

arXiv2025

Optimized Schwarz method for the Stokes-Darcy problem with generalized interface conditions

Due to their wide appearance in environmental settings as well as industrial and medical applications, the Stokes-Darcy problems with different sets of interface conditions establish an active research area in the community of mathematical modelers and computational scientists. For numerical simulation of such coupled problems in applications, robust and efficient computational algorithms are needed. In this work, we consider a generalization of the Beavers-Joseph interface condition recently developed using homogenization and boundary layer theory. This extension is applicable not only for the parallel flows to the fluid-porous interface as its predecessor, but also for arbitrary flow directions. To solve the Stokes-Darcy problem with these generalized interface conditions efficiently, we develop and analyze a Robin-Robin domain decomposition method using Fourier analysis to identify optimal weights in the Robin interface conditions. We study efficiency and robustness of the proposed method and provide numerical simulations which confirm the obtained theoretical results.

math.NA↗

arXiv2024

Efficient preconditioners for coupled Stokes-Darcy problems with MAC scheme: Spectral analysis and numerical study

Coupled systems of free flow and porous media arise in a variety of technical and environmental applications. For laminar flow regimes, such systems are described by the Stokes equations in the free-flow region and Darcy's law in the porous medium. An appropriate set of coupling conditions is needed on the fluid-porous interface. Discretisations of the Stokes-Darcy problems yield large, sparse, ill-conditioned, and, depending on the interface conditions, non-symmetric linear systems. Therefore, robust and efficient preconditioners are needed to accelerate convergence of the applied Krylov method. In this work, we consider the second order MAC scheme for the coupled Stokes-Darcy problems and develop and investigate block diagonal, block triangular and constraint preconditioners. We apply two classical sets of coupling conditions considering the Beavers-Joseph and the Beavers-Joseph-Saffman condition for the tangential velocity. For the Beavers-Joseph interface condition, the resulting system is non-symmetric, therefore GMRES method is used for both cases. Spectral analysis is conducted for the exact versions of the preconditioners identifying clusters and bounds. Furthermore, for practical use we develop efficient inexact versions of the preconditioners. We demonstrate effectiveness and robustness of the proposed preconditioners in numerical experiments.

math.NA↗

arXiv2022

A modification of the Beavers-Joseph condition for arbitrary flows to the fluid-porous interface

Physically consistent coupling conditions at the fluid-porous interface with correctly determined effective parameters are necessary for accurate modeling and simulation of various applications. To describe single-fluid-phase flows in coupled free-flow and porous-medium systems, the Stokes/Darcy equations are typically used together with the conservation of mass across the interface, the balance of normal forces and the Beavers-Joseph condition on the tangential velocity. The latter condition is suitable for flows parallel to the interface but not applicable for arbitrary flow directions. Moreover, the value of the Beavers-Joseph slip coefficient is uncertain. In the literature, it is routinely set equal to one that is not correct for many applications, even if the flow is parallel to the porous layer. In this paper, we reformulate the generalized interface condition on the tangential velocity component, recently developed for arbitrary flows in Stokes/Darcy systems, such that it has the same analytical form as the Beavers-Joseph condition. We compute the effective coefficients appearing in this modified condition using theory of homogenization with boundary layers. We demonstrate that the modified Beavers-Joseph condition is applicable for arbitrary flow directions to the fluid-porous interface. In addition, we propose an efficient two-level numerical algorithm based on simulated annealing to compute the optimal Beavers-Joseph parameter.

physics.flu-dyn↗