A Newton method using exact jacobians for solving fluid-structure coupling

By M. Fernández, M. Moubachir. 2005

346 citations recorded by the source corpus.

This paper aims at introducing a partitioned Newton based method for solving nonlinear coupled systems arising in the numerical approximation of fluid-structure interaction problems. We provide a method which characteristic lies in the use of exact cross jacobians evaluation involving the shape derivative of the fluid state with respect to solid motion perturbations. Numerical tests based on an implementation inside a 3D fluid-structure interaction code show how the exactness of the cross jacobians computation guarantee the overall convergence of the Newton's loop.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/e04361efd124445d9778a72fe778c0cacb453a12

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In Computational Mechanics

Citations in the corpus

Performance of partitioned procedures in fluid-structure interaction (2010, background): “[24] rewrote the fluid-structure problem as a nonlinear problem in the state of the structure, with the flow state as internal variables of the pr oblem.”
Isogeometric Fluid–structure Interaction Analysis with Applications to Arterial Blood Flow (2006, background): “Applications of ALE to hemodynamics are discussed in [12, 15, 16, 31] and referen c s therein.”
A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping (2012, methodology): “In order to enhance convergence during sub-iterations, the Newton method using exact Jacobians has also been tested in [11].”
Truly monolithic algebraic multigrid for fluid–structure interaction (2011, methodology): “We compare the two AMG preconditioners introduced in Sections 6 and 7 with each other, the iteratively staggered Aitken method [14] as well as to an Interface Jacobian-free Newton–Krylov method proposed in [11].”
Partitioned solver for strongly coupled fluid–structure interaction (2013, methodology): “used coupling methods are the fixed-point method (also called block Gauss–Seidel method) [19–21], the interface Newton–Krylov and the quasi-Newton methods [21–25].”
Stabilization of explicit coupling in fluid-structure interaction involving fluid incompressibility (2009, methodology): “In order to facilitate the analysis and to motivate de different coupling schemes introduced in this paper, we first consider a low Reynolds regime and assume that the interface undergoes infinitesimal displacements.”
Isogeometric fluid-structure interaction: theory, algorithms, and computations (2008, neutral): “, [15,19]).”
Fixed-point fluid–structure interaction solvers with dynamic relaxation (2008, methodology): “In comparison to [10], however, the Aitken method requires only a moderate number of iterations and only needs approximately 1.”
Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect (2008, methodology): “The use of a full Newton algorithm is suggested in [14].”
A projection semi‐implicit scheme for the coupling of an elastic structure with an incompressible fluid (2007, methodology): “cheap, since they do not require the computation of shape (domain) derivatives (see [22]).”
Curvilinear Immersed Boundary Method for Simulating Fluid Structure Interaction with Complex 3D Rigid Bodies (2008, methodology): “Based on these results the lock-in region for this system is Ured 2 [4,7] with maximum vibration amplitude of about 0.”
Stability of a coupling technique for partitioned solvers in FSI applications (2008, neutral): “The fluid-structure interaction problem in the latter formulation can be solved with Newton-Raphson iterations [15,16].”
Performance of a new partitioned procedure versus a monolithic procedure in fluid-structure interaction (2009, background): “The first case is the wave propagation in a straight, threedimensional elastic tube [32].”
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.”