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1: Arbitrary solid edge along the FSI interface

1: Arbitrary solid edge along the FSI interface

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Thesis
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This work details the development of a computational tool that can accurately model strongly-coupled fluid-structure-interaction (FSI) problems, with a particular focus on thin-walled structures undergoing large, geometrically non-linear deformations, which has a major interest in, amongst others, the aerospace and biomedical industries. The first...

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Citations

... Given the set of equations, the monolithic approach casts the governing equations (including the interface conditions) in terms of the same primitive variables, and discretises the entire domain using the same numerical procedure [9,55]. Due to the limitations of the FVM when applied to the structural equations [93,98], this is typically done using the FEM. The equations are then cast into a system of linear equations, and usually solved using some variant of Newton's method. ...
... Following the work of Suliman [98], let us consider the piston-channel problem as a 1D spring-mass system, where the piston acts as a linear spring, and the incompressible uid as a variable mass system. Based on the balance of forces along the interface, it is possible to construct an expression for the interface displacement d Γ and interface velocity u Γ ∂d Γ ∂t = u Γ , ...
Thesis
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In this thesis, the development of a strongly coupled, partitioned fluid-structure interactions (FSI) solver is outlined. Well established methods are analysed and new methods are proposed to provide robust, accurate and efficient FSI solutions. All the methods introduced and analysed are primarily geared towards the solution of incompressible, transient FSI problems, which facilitate the use of black-box sub-domain field solvers. In the first part of the thesis, radial basis function (RBF) interpolation is introduced for interface information transfer. RBF interpolation requires no grid connectivity information, and therefore presents an elegant means by which to transfer information across a non-matching and non-conforming interface to couple finite element to finite volume based discretisation schemes. The transfer scheme is analysed, with particular emphasis on a comparison between consistent and conservative formulations. The primary aim is to demonstrate that the widely used conservative formulation is a zero-order method. Furthermore, while the consistent formulation is not provably conservative, it yields errors well within acceptable levels and converges within the limit of mesh refinement. A newly developed multi-vector update quasi-Newton (MVQN) method for implicit coupling of black-box partitioned solvers is proposed. The new coupling scheme, under certain conditions, can be demonstrated to provide near Newton-like convergence behaviour. The superior convergence properties and robust nature of the MVQN method are shown in comparison to other well known quasi-Newton coupling schemes, including the least squares reduced order modelling (IBQN-LS) scheme, the classical rank-1 update Broyden's method, and fixed point iterations with dynamic relaxation. Partitioned, incompressible FSI, based on Dirichlet-Neumann domain decomposition solution schemes, cannot be applied to problems where the fluid domain is fully enclosed. A simple example often provided in the literature is that of balloon inflation with a prescribed inflow velocity. In this context, artificial compressibility (AC) will be shown to be a useful method to relax the incompressibility constraint, by including a source term within the fluid continuity equation. The attractiveness of AC stems from the fact that this source term can readily be added to almost any fluid field solver, including most commercial solvers. AC/FSI is however limited in the range of problems it can effectively be applied to. To this end, the combination of the newly developed MVQN method with AC/FSI is proposed. In so doing, the AC modified fluid field solver can continue to be treated as a black-box solver, while the overall robustness and performance are significantly improved. The study concludes with a demonstration of the modularity offered by partitioned FSI solvers. The analysis of the coupled environment is extended to include steady state FSI, FSI with free surfaces and an FSI problem with solid-body contact.
... Following the work of Suliman [27], let us consider the piston-channel prob- Table 1: Comparison of the number of iterations and relative computational time for the exible tail problem, for dierent time steps sizes and convergence criterion . The notation IBQN-LS(q) indicates information from q preceding time steps are retained. ...
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