Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction

The interaction between a fluid and a poroelastic structure is a complex problem that couples the Navier-Stokes equations with the Biot system. The finite element approximation of this problem is involved due to the fact that both subproblems are indefinite. In this work, we first design residual-based stabilization techniques for the Biot system, motivated by the variational multiscale approach. Then, we state the monolithic Navier-Stokes/Biot system with the appropriate transmission conditions at the interface. For the solution of the coupled system, we adopt both monolithic solvers and heterogeneous domain decomposition strategies. Different domain decomposition methods are considered and their convergence is analyzed for a simplified problem. We compare the efficiency of all the methods on a test problem that exhibits a large added-mass effect, as it happens in hemodynamics applications. (C) 2009 Elsevier Inc. All rights reserved.

Parallel Algorithms for the Solution of Large-Scale Fluid-Structure Interaction Problems in Hemodynamics

Davide Forti

This thesis addresses the development and implementation of efficient and parallel algorithms for the numerical simulation of Fluid-Structure Interaction (FSI) problems in hemodynamics. Indeed, hemodynamic conditions in large arteries are significantly affected by the interaction of the pulsatile blood flow with the arterial wall. The simulation of fluid-structure interaction problems requires the approximation of a coupled system of Partial Differential Equations (PDEs) and the set up of efficient numerical solution strategies. Blood is modeled as an incompressible Newtonian fluid whose dynamics is governed by the Navier-Stokes equations. Different constituive models are used to describe the mechanical response of the arterial wall; specifically, we rely on hyperelastic isotropic and anistotropic material laws. The finite element method is used for the space discretization of both the fluid and structure problems. In particular, for the Navier-Stokes equations we consider a semi-discrete formulation based on the Variational Multiscale (VMS) method. Among a wide range of possible solution strategies for the FSI problem, here we focus on strongly coupled monolithic approaches wherein the nonlinearities are treated in a fully implicit mode. To cope with the high computational complexity of the three dimensional FSI problem, a parallel solution framework is often mandatory. To this end, we develop a new block parallel preconditioner for the coupled linearized FSI system obtained after space and time discretization. The proposed preconditioner, named FaCSI, exploits the factorized form of the FSI Jacobian matrix, the use of static condensation to formally eliminate the interface degrees of freedom of the fluid equations, and the use of a SIMPLE preconditioner for unsteady Navier-Stokes equations. In FSI problems, the different resolution requirements in the fluid and structure physical domains, as well as the presence of complex interface geometries make the use of matching fluid and structure meshes problematic. In such situations, it is much simpler to deal with discretizations that are nonconforming at the interface, provided however that the matching conditions at the interface are properly fulfilled. In this thesis we develop a novel interpolation-based method, named INTERNODES, for numerically solving partial differential equations by Galerkin methods on computational domains that are split into two (or several) subdomains featuring nonconforming interfaces. By this we mean that either a priori independent grids and/or local polynomial degrees are used to discretize each subdomain. INTERNODES can be regarded as an alternative to the mortar element method: it combines the accuracy of the latter with the easiness of implementation in a numerical code. The aforementioned techniques have been applied for the numerical simulation of large-scale fluid-structure interaction problems in the context of biomechanics. The parallel algorithms developed showed scalability up to thousands of cores utilized on high performance computing machines.

EPFL2016

Iterative solutions of multimodels for incompressible flows

Alfio Quarteroni

Summary: For the simulation of two-dimensional incompressible flows, the Navier-Stokes equations can be coupled with models of reduced complexity, such as Oseen and Stokes models. This approach is briefly reviewed here. Then we propose a numerical solution of the coupled problem by subdomain splitting. We give numerical results obtained by finite element and spectral element approximations on a couple of test problems of physical interest.

World Scientific2000

Public urban transport in the context of social inclusion and cohesion – the case of Santiago de Chile

Regina Witter

What are the impacts of a re-designed public transportation system in a city where social differences are heavily manifested in spatial separation, i.e. where exist certain inequalities concerning the access to daily activities and participation in urban life? Are the changes just of transport-related manner, resulting in changes in accessibility conditions? Or might there be further impacts on people’s mobility behaviour, or even on economic and spatial structures within the city, affecting the manifestation or dissolution of social differences? What, moreover, happens, if the new system presents a set of functioning problems, and the systematic changes are very drastic, neglecting existent peoples’ preferences and habits concerning the entire urban transport system, including private modes? What are the concrete reasons for people’s lack of capability to cope with the new system? Finally, are there any measures to be implemented to support the societal acceptance of the new transportation system, in favour of a profitable exploitation, social interaction among users and thus, social cohesion? These are the main interests of the PhD-related research presented in this article, giving some insights into the theoretical framework, the methodological approach and first findings concerning the “role of public urban transport in the context of social inclusion and cohesion”. The PhD has recently been started at the EPFL in Lausanne/Switzerland and is principally based on the case study area of Santiago de Chile. There the national government implemented in February 2007 the new Transantiago system, representing an ambitious approach to substitute the previous rather de-regulated low-quality service by a modern and efficient one. So a new trunk and feeder line network was re-designed from scratch, whose main skeleton is constituted by the existent public metro service and complemented by privately operated bus lines. Unfortunately, the first experiences with the Transantiago have been merely negative, due to a set of technical and institutional problems and further social and cultural obstacles. Even if the national authorities committed to implement all design modifications as soon as possible, some problems are expected to remain also in a long term. Today, the Transantiago presents a hot topic in political debates and everyone’s daily life discussions. After the subsequent theoretical insights, the case study area of Santiago de Chile is presented, describing the urban development framework, the previous transportation service and the main problems related to the new Transantiago system. On this basis the research hypothesizes and objectives as well as the methodological approach are introduced. The final part offers some first findings for the Santiago case and bridges to the conference topic dealing with spatial inequalities due to public action.