Numerical approximation of fluid-structure interaction problems with application to haemodynamics

By Fabio Nobile. 2001

316 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/16756e3836701dc2a64cbb9c2255478a36558b00

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Convergence of a finite element/ALE method for the Stokes equations in a domain depending on time (2009, methodology): “In the casewhere thedomain is time dependent but given, the convergence analysis for the ALE method has been considered by [14–16], in the case of the advection–diffusion equation instead of the Stokes or the Navier–Stokes equations.”
A projection semi‐implicit scheme for the coupling of an elastic structure with an incompressible fluid (2007, background): “In the present work, we are interested in those cases where the classical weakly coupled schemes are apparently unstable, as observed in various numerical studies (for instance [38, 32, 40, 26]).”
Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity (2006, background): “In the case of linear structural dynamics, Eq.”
Isogeometric fluid-structure interaction: theory, algorithms, and computations (2008, background): “For precise conditions on the regularity of the ALE map, see Nobile [51].”
Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect (2008, methodology): “The fluid and structure physical parameters used in the simulations are listed in Table 1: a double line separates the common ones from the ones of the 2d problem only (see [23]), which are separated also from the parameters of the 3d problem (see [11]).”
Stabilization of explicit coupling in fluid-structure interaction involving fluid incompressibility (2009, methodology): “…0, in Ωf , ∇ · u = 0, in Ωf , u = ū, on Γin, σ(u, p)n = g, on Γout, (1) ρs∂ 2 ttη −∇ · σs(η) = 0, in Ωs, η = 0, on Γd, σs(η)ns = 0, on Γn, (2) INRIA Stabilized explicit coupling in FSI with fluid incompressibility 5 satisfying the interface coupling conditions{ u = ∂tη, on Σ, σs(η)ns = −σ(u,…”
Added-mass effect in the design of partitioned algorithms for fluid-structure problems (2005, methodology): “2 Motivations In order to motivate the main results of this article, we recall some empirical observations made on a basic FSI test case proposed in previous studies (see [6, 7, 16]).”
Fluid-structure partitioned procedures based on Robin transmission conditions (2008, methodology): “[15,8]), or treat the interface position and the convective term in an explicit way by extrapolation from previous time steps (semi-implicit algorithm, see, e.”
Stability analysis of second-order time accurate schemes for ALE-FEM (2004, unknown): “More details may be found in [10].”
Isogeometric Fluid–structure Interaction Analysis with Applications to Arterial Blood Flow (2006, background): “For a general discussion of ALE, the reader is referred to [8‐10, 22, 29] and references there in. Applications of ALE to hemodynamics are discussed in [12, 15, 16, 31 ] and references therein.”
ACCELERATION OF A FIXED POINT ALGORITHM FOR FLUID-STRUCTURE INTERACTION USING TRANSPIRATION CONDITIONS (2003, methodology): “Standard strategies to solve this non-linear system are fixed-point based methods as Block-Jacobi or Block-Gauss-Seidel (BGS) iterations, see [3,14,17,19].”