Stokes-Darcy boundary integral solutions using preconditioners

Authors:
Yassine Boubendir;Svetlana Tlupova
Affiliations:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, 323 Dr. Martin Luther King, Jr. Boulevard, University Heights, Newark, NJ ...;Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, 323 Dr. Martin Luther King, Jr. Boulevard, University Heights, Newark, NJ ...
Venue:
Journal of Computational Physics
Year:
2009

Citing 14
Cited 1

Improved volume conservation in the computation of flows with immersed elastic boundaries

Journal of Computational Physics
Integral equation methods for Stokes flow and isotropic elasticity in the plane

Journal of Computational Physics
On the interface boundary condition of Beavers, Joseph, and Saffman

SIAM Journal on Applied Mathematics
The Method of Regularized Stokeslets

SIAM Journal on Scientific Computing
A Method for Computing Nearly Singular Integrals

SIAM Journal on Numerical Analysis
A Robust Finite Element Method for Darcy--Stokes Flow

SIAM Journal on Numerical Analysis
Coupling Fluid Flow with Porous Media Flow

SIAM Journal on Numerical Analysis
Mathematical and numerical models for coupling surface and groundwater flows

Applied Numerical Mathematics
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
A unified stabilized method for Stokes' and Darcy's equations

Journal of Computational and Applied Mathematics
Robin-Robin Domain Decomposition Methods for the Stokes-Darcy Coupling

SIAM Journal on Numerical Analysis
On the evaluation of layer potentials close to their sources

Journal of Computational Physics
The method of images for regularized Stokeslets

Journal of Computational Physics
Boundary integral solutions of coupled Stokes and Darcy flows

Journal of Computational Physics

Splitting extrapolation algorithms for solving the boundary integral equations of anisotropic Darcy's equation on polygons by mechanical quadrature methods

Numerical Algorithms

Quantified Score

Hi-index	31.45

Visualization

Abstract

In a system where a free fluid flow is coupled to flow in a porous medium, different PDEs are solved simultaneously in two subdomains. We consider steady Stokes equations in the free region, coupled across a fixed interface to Darcy equations in the porous substrate. Recently, the numerical solution of this system was obtained using the boundary integral formulation combined with a regularization-correction procedure. The correction process also results in the improvement of the condition number of the linear system. In this paper, an appropriate preconditioner based on the singular part of corrections is introduced to improve the convergence of a Krylov subspace method applied to solve the integral formulation.