An efficient solver for the fully coupled solution of large-displacement fluid–structure interaction problems

Fluid-structure interaction (FSI) problems are computationally very challenging. In this paper we consider the monolithic approach for solving the fully coupled FSI problem. Most existing techniques, such as multigrid methods, do not work well for the coupled system since the system consists of elliptic, parabolic and hyperbolic components all together. Other approaches based on direct solvers do not scale to large numbers of processors. In this paper, we introduce a multilevel unstructured mesh Schwarz preconditioned Newton–Krylov method for the implicitly discretized, fully coupled system of partial differential equations consisting of incompressible Navier–Stokes equations for the fluid flows and the linear elasticity equation for the structure. Several meshes are required to make the solution algorithm scalable. This includes a fine mesh to guarantee the solution accuracy, and a few isogeometric coarse meshes to speed up the convergence. Special attention is paid when constructing and partitioning the preconditioning meshes so that the communication cost is minimized when the number of processor cores is large. We show numerically that the proposed algorithm is highly scalable in terms of the number of iterations and the total compute time on a supercomputer with more than 10,000 processor cores for monolithically coupled three-dimensional FSI problems with hundreds of millions of unknowns.

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Parametric Analysis of Eustachian Tube Function Using Fully Coupled Fluid-Structure Interaction Models

ASME 2010 Summer Bioengineering Conference, Parts A and B ◽

10.1115/sbc2010-19425 ◽

2010 ◽

Author(s):

Francis J. Sheer ◽

Samir N. Ghadiali

Keyword(s):

Eustachian Tube ◽

Healthy Adult ◽

Fluid Structure Interaction ◽

Fluid Structure ◽

Structure Interaction ◽

Related Cost ◽

Tube Function ◽

Histological Images ◽

Fully Coupled ◽

Onset Rate

Otitis Media (OM) is the most commonly diagnosed childhood illness and has health care related cost of four billion dollars annually. [1] The onset of OM has been directly related to Eustachian Tube (ET) dysfunction. The ET has three main physiological functions, and when these functions are compromised, middle ear (ME) disorders arise. It is also known that specific populations of patients, such as those with cranio-facial abnormalities, such as a cleft palate, have a 100% onset rate of OM. Even though ET dysfunction has been related to OM, the underlying reasons for ET dysfunction in certain populations remains unknown. To gain an understanding of this system, we use fully coupled fluid-structure interaction (FSI) models of the ET based on geometries reconstructed from histological images. Using these models in systematic parameter variation studies allows us to identify which parameters of the ET can cause dysfunction. Using healthy adult subjects as a model for a well-functioning ET, we determined ET function to be sensitive to changes in TVP muscle force.

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