Added-mass effect in the design of partitioned algorithms for fluid–structure problems

Causin, Paola; Gerbeau, Jean-Frédéric; Nobile, Fabio

doi:10.1016/j.cma.2004.12.005

Cited by 708 publications

(815 citation statements)

References 13 publications

Supporting

Mentioning

776

Contrasting

Unclassified

Order By: Relevance

“…Such a block Gauss-Seidel iterative scheme provides strong coupling of the partitioned fluid and structure subproblems and, when implemented in conjunction with the implicit dual timestepping the scheme of the fluid solver and implicit Newmark/Newton-Raphson scheme of the structural solver, enables a large physical time step to be maintained. Depending upon the time step selected and/or the combined physical and geometrical parameters of the problem-certain classes of problem frequently encountered in biomedical modelling can be severely destabilized by the effects of the so-called added-mass phenomena [41,42]-subiterations may or may not be required at each time level for strong coupling to be achieved. In the examples presented here, matching discretizations have been generated at the interface to avoid the errors associated with data interpolation on highly non-matching discretizations during this implementation stage.…”

Section: Partitioned Fluid-structure Interface Couplingmentioning

confidence: 99%

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

Wood

Gil

Hassan

et al. 2008

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYThis paper presents a fully coupled three-dimensional solver for the analysis of time-dependent fluidstructure interaction. A partitioned time-marching algorithm is employed for the solution to the timedependent coupled discretized problem, thus enabling the use of highly developed, robust and well-tested solvers for each field. Coupling of the fields is achieved through a conservative transfer of information at the fluid-structure interface. An implicit coupling is achieved when the solutions to the fluid and structure subproblems are cycled at each time step until convergence is reached. The three-dimensional unsteady incompressible fluid is solved using a powerful implicit dual time-stepping technique with an explicit multistage Runga-Kutta time stepping in pseudo-time and arbitrary Lagrangian-Eulerian formulation for the moving boundaries. A finite element dynamic analysis of the highly deformable structure is carried out with a numerical strategy combining the implicit Newmark time integration algorithm with a NewtonRaphson second-order optimization method. Various test cases are presented for benchmarking and to demonstrate the potential applications of this method.

show abstract

Section: Partitioned Fluid-structure Interface Couplingmentioning

confidence: 99%

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

Wood

Gil

Hassan

et al. 2008

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

“…It has been shown in several studies [8,7,9] that the instability of the coupling iterations within the time step has a physical cause. Consequently, the time discretization schemes are not expected to have much influence on the stability of the coupling iterations although they will influence the final result of the coupling iterations.…”

Section: Introductionmentioning

confidence: 99%

“…Förster et al [7] analyzed the effect of these parameters on algorithms without coupling iterations. Causin et al [8] studied algorithms with and without coupling iterations and derived the maximal relaxation factor that leads to convergence of coupling iterations as a function of the aforementioned parameters for a simplified model of blood flow in an artery and then validated the formulas with numerical experiments. Degroote et al [9] analyzed a more simplified model for the artery and performed a modal decomposition of the interface's displacement during the coupling iterations.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of Gauss–Seidel iterations in a partitioned simulation of fluid–structure interaction

Degroote

Annerel

Vierendeels

2010

Computers & Structures

View full text Add to dashboard Cite

A stability analysis of Gauss-Seidel coupling iterations for partitioned simulation of fluid-structure interaction is performed for the flow in a flexible tube. In a previous study the inertia of the structure and the interaction between the segments of the structure were not taken into account. It is now demonstrated that especially the structural inertia has a significant effect on the stability of Gauss-Seidel iterations for a certain range of the time step's size.

show abstract

“…In [32] it was reported that the stability of explicit coupled algorithms is also influenced by the geometry of the domain and the material properties, in particular the involved densities and their ratios. The study of these dependencies will be further work.…”

Section: Discussionmentioning

confidence: 99%

Flow simulation on moving boundary-fitted grids and application to fluid-structure interaction problems

Engel

Griebel

2005

Int. J. Numer. Meth. Fluids

View full text Add to dashboard Cite

SUMMARYWe present a method for the parallel numerical simulation of transient three-dimensional fluidstructure interaction problems. Here, we consider the interaction of incompressible flow in the fluid domain and linear elastic deformation in the solid domain. The coupled problem is tackled by an approach based on the classical alternating Schwarz method with non-overlapping subdomains, the subproblems are solved alternatingly and the coupling conditions are realized via the exchange of boundary conditions. The elasticity problem is solved by a standard linear finite element method. A main issue is that the flow solver has to be able to handle time-dependent domains. To this end, we present a technique to solve the incompressible Navier-Stokes equation in three-dimensional domains with moving boundaries. This numerical method is a generalization of a finite volume discretization using curvilinear coordinates to time-dependent coordinate transformations. It corresponds to a discretization of the Arbitrary Lagrangian-Eulerian formulation of the Navier-Stokes equations. Here the grid velocity is treated in such a way that the so-called Geometric Conservation Law is implicitly satisfied. Altogether, our approach results in a scheme which is an extension of the well-known MACmethod to a staggered mesh in moving boundary-fitted coordinates which uses grid-dependent velocity components as the primary variables.To validate our method, we present some numerical results which show that second order convergence in space is obtained on moving grids. Finally, we give the results of a fully coupled fluidstructure interaction problem. It turns out that already a simple explicit coupling with one iteration of the Schwarz method, i.e. one solution of the fluid problem and one solution of the elasticity problem per time step, yields a convergent, simple, yet efficient overall method for fluid-structure interaction problems.

show abstract

Added-mass effect in the design of partitioned algorithms for fluid–structure problems

Abstract: Nobile. Added-mass effect in the design of partitioned algorithms for fluid-structure problems.

Cited by 708 publications

References 13 publications

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

Stability analysis of Gauss–Seidel iterations in a partitioned simulation of fluid–structure interaction

Flow simulation on moving boundary-fitted grids and application to fluid-structure interaction problems

Contact Info

Product

Resources

About