Paula Strohbeck, SFB 1313 doctoral researcher at the Institute of Applied Analysis and Numerical Simulation (research project A03), will give her milestone presentation on "Efficient solution strategies for coupled free-flow and porous-medium problems" on 6 September 2024.
Date: Friday, 6 September 2024
Time: 11 am CET
Title: "Efficient solution strategies for coupled free-flow and porous-medium problems"
Place: Pfaffenwaldring 57, room 7.133, University of Stuttgart, Campus Vaihingen, 70569, Stuttgart.
Abstract
Coupled systems of porous media and free flow arise in a variety of applications, e.g. industrial filtration, blood flow in the human body, and surface/subsurface interactions. Such flow problems are usually described by the Stokes equations in the free-flow domain, Darcy’s law in the porous medium, and a suitable set of coupling conditions on the fluid–porous interface. We develop efficient solution strategies for the coupled Stokes–Darcy system with the classical set of coupling conditions based on either the Beavers–Joseph–Saffman or the Beavers–Joseph condition, and the generalised interface conditions.To accelerate solving the coupled problem in a monolithic way, we consider preconditioning techniques. We present several preconditioners and conduct spectral and field-of-values analysis of the preconditioned systems to show the accelerated convergence of the iterative method. Direct use of the exact preconditioners is computationally expensive. Thus, we also determine inexact variants of the constructed preconditioners.Alternatively, we take advantage of the multi-physics and multi-domain nature of the problem through domain decomposition methods. Specifically, we develop a Robin-Robin method for the Stokes–Darcy system with the generalized coupling conditions. Its convergence properties are analysed and optimal Robin parameters for the interface conditions are derived. We demonstrate the effectiveness and robustness of the two proposed solution strategies in numerical experiments.