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Abstract - Domain decomposition methods for multiphysic problems

Author: Marco Discacciati

Title of the contribution: Domain decomposition methods for multiphysic problems

Abstract:
In this talk we illustate the application of domain decomposition methods to heterogeneous coupled problems defined in nonoverlapping regions.

In particular, in the first part of the talk we will consider the coupling of surface and groundwater flows.

The problem is defined in a computational domain split into a fluid region and a porous media subdomain. The Navier-Stokes equations are considered for modeling the fluid flows, while Darcy's equations describe the filtration through the porous media. By exploiting the so-called Beavers and Joseph interface conditions, we will assess the well-posedness of the global problem and show that it can be expressed as an interface equation involving nonlinear local Steklov-Poincaré operators. Finally, we will illustrate possible iterative substructuring methods to solve the coupled problem.

In the second part of the talk, we will apply the theoretical framework that we have studied to a fluid-structure interaction problem arising in hemodynamics for modeling blood flows in large arteries. Possible iterative methods to solve this problem will be presented together with some numerical results.

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