125 research outputs found
On the existence and the uniqueness of the solution to a fluid-structure interaction problem
In this paper we consider the linearized version of a system of partial
differential equations arising from a fluid-structure interaction model. We
prove the existence and the uniqueness of the solution under natural regularity
assumptions
Higher-order time-stepping schemes for fluid-structure interaction problems
We consider a recently introduced formulation for fluid-structure interaction
problems which makes use of a distributed Lagrange multiplier in the spirit of
the fictitious domain method. In this paper we focus on time integration
methods of second order based on backward differentiation formulae and on the
Crank-Nicolson method. We show the stability properties of the resulting
method; numerical tests confirm the theoretical results
Unfitted mixed finite element methods for elliptic interface problems
In this paper, new unfitted mixed finite elements are presented for elliptic
interface problems with jump coefficients. Our model is based on a fictitious
domain formulation with distributed Lagrange multiplier. The relevance of our
investigations is better seen when applied to the framework of fluid structure
interaction problems. Two finite elements schemes with piecewise constant
Lagrange multiplier are proposed and their stability is proved theoretically.
Numerical results compare the performance of those elements, confirming the
theoretical proofs and verifying that the schemes converge with optimal rate.Comment: 29 pages, 16 figures, 18 table
Immersed boundary method: performance analysis of popular finite element spaces
The aim of this paper is to understand the performances of different finite elements
in the space discretization of the Finite Element Immersed Boundary Method. In
this exploration we will analyze two popular solution spaces: Hood-Taylor and Bercovier-
Pironneau (P1-iso-P2). Immersed boundary solution is characterized by pressure discontinuities
at fluid structure interface. Due to such a discontinuity a natural enrichment
choice is to add piecewise constant functions to the pressure space. Results show that
P1 + P0 pressure spaces are a significant cure for the well known “boundary leakage”
affecting IBM. Convergence analysis is performed, showing how the discontinuity in the
pressure is affecting the convergence rate for our finite element approximation
A parallel solver for FSI problems with fictitious domain approach
We present and analyze a parallel solver for the solution of fluid structure
interaction problems described by a fictitious domain approach. In particular,
the fluid is modeled by the non-stationary incompressible Navier-Stokes
equations, while the solid evolution is represented by the elasticity
equations. The parallel implementation is based on the PETSc library and the
solver has been tested in terms of robustness with respect to mesh refinement
and weak scalability by running simulations on a Linux cluster.Comment: Contribution to the 5th African Conference on Computational Mechanic
Mass preserving distributed langrage multiplier approach to immersed boundary method
This research is devoted to mass conservation and CFL properties of the
Finite Elements Immersed Boundary Method. We first explore an enhanced higher order
scheme applied to the Finite Element Immersed Boundary Method technique introduced
by Boffi and Gastaldi. This technique is based on a Pointwise (PW) formulation of the
kinematic condition, and higher order elements show better conservation properties than
the original scheme. A further improvement with respect to the classical PW formulation
is achieved introducing a fully variational Distributed Lagrange Multiplier (DLM) formulation.
Numerical experiments show that DLM is not affected by any CFL condition.
Furthermore the mass conservation properties of this method are extremely competitive
A parallel solver for fluid structure interaction problems with Lagrange multiplier
The aim of this work is to present a parallel solver for a formulation of
fluid-structure interaction (FSI) problems which makes use of a distributed
Lagrange multiplier in the spirit of the fictitious domain method. The fluid
subproblem, consisting of the non-stationary Stokes equations, is discretized
in space by - finite elements, whereas the
structure subproblem, consisting of the linear or finite incompressible
elasticity equations, is discretized in space by finite
elements. A first order semi-implicit finite difference scheme is employed for
time discretization. The resulting linear system at each time step is solved by
a parallel GMRES solver, accelerated by block diagonal or triangular
preconditioners. The parallel implementation is based on the PETSc library.
Several numerical tests have been performed on Linux clusters to investigate
the effectiveness of the proposed FSI solver.Comment: 27 pages, 8 figures, 14 table
- …