A Quasi-Newton Algorithm Based on a Reduced Model for Fluid-Structure Interaction Problems in Blood Flows

Abstract

Abstract.We propose a quasi-Newton algorithm for solving fluid-structure interaction problems.The basic idea of the method is to build an approximate tangent operator which is cost effective and which takes into account the so-called added mass effect. Various test cases show that the method allows a significant reduction of the computational effort compared to relaxed fixed point algorithms. We present 2D and 3D fluid-structure simulations performed either with a simple 1D structure model or with shells in large displacements.Mathematics Subject Classification. 65M60, 74K25, 76D05, 76Z05.

Stabilized explicit coupling for fluid–structure interaction using Nitsche's method

“…Computational Fluid-Structure Dynamics (CFSD) is of great importance in practically all engineering fields, from aeroelasticity to bio-mechanics problems (see, for instance, [28,10,11,24,30,27,32,17,14,38,2] and the references therein).…”

“…Up to now, these instabilities have been overcome mainly through the use of implicit coupling (or strongly coupled) schemes (see [26,17,13,14,8,1] and the references therein). Such an approach leads to a fully coupled problem at each time step, the solution of which often requires a huge computational effort.…”

Partitioned solution of an unsteady adjoint for strongly coupled fluid-structure interactions and application to parameter identification of a one-dimensional problem

“…For the structure, a so-called generalised string model is applied. This model is derived from the linear elasticity theory for a cylindrical tube with small thickness under the assumption of membrane deformations [1,42]. It disregards the axial and circumferential displacement of the tube wall.…”

“…The other coefficients are the shear modulus G, the Young modulus E and the Poisson coefficient ν. The viscoelastic term is further omitted (γ = 0), which is a common simplification [42]. The Timoshenko shear correction factor κ is calculated from the Poisson coefficient [43], although it is now understood that this correction factor alone cannot always account precisely for dynamic analyses of beams with arbitrary and inhomogeneous cross sections [44].…”

“…With the definition of the cost function in Equation 39, the parameter identification can be reformulated as a minimisation problem min s,x j(s, x) (42) subject to the governing equations as constraints r(s, x) = 0.…”