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 part of this work investigates improving the efficiency with which a stable and robust in-house code, Elemental, models thin structures undergoing dynamic fluid-induced bending deformations. Variations of the existing finite volume formulation as well as linear and higher-order finite element formulations are implemented. The governing equations for the solid domain are formulated in a total Lagrangian or undeformed conguration and large geometrically non-linear deformations are accounted for. The set of equations is solved via a single-step Jacobi iterative scheme which is implemented such as to ensure a matrix-free and robust solution. Second-order accurate temporal discretisation is achieved via dual-timestepping, with both consistent and lumped mass matrices and with a Jacobi pseudo-time iteration method employed for solution purposes. The matrix-free approach makes the scheme particularly well-suited for distributed memory parallel hardware architectures. Three key outcomes, not well documented in literature, are highlighted: the issue of shear locking or sensitivity to element aspect ratio, which is a common problem with the linear Q4 finite element formulation when subjected to bending, is evaluated on the finite volume formulations; a rigorous comparison of finite element vs. finite volume methods on geometrically non-linear structures is done; a higher-order finite volume solid mechanics procedure is developed and evaluated. The second part of this work is concerned with fluid-structure interaction (FSI) modelling. It considers the implementation and coupling of a higher order finite element structural solver with the existing finite volume fluid-flow solver in Elemental. To the author’s knowledge, this is the first instance in which a strongly-coupled hybrid finite element–finite volume FSI formulation is developed. The coupling between the fluid and structural components with non-matching nodes is rigorously assessed. A new partitioned fluid-solid interface coupling methodology is also developed, which ensures stable partitioned solution for strongly-coupled problems without any additional computational overhead. The solver is parallelised for distributed memory parallel hardware architectures. The developed technology is successfully validated through rigorous temporal and mesh independent studies of representative two-dimensional strongly-coupled large-displacement FSI test problems for which analytical or benchmark solutions exist.
Dissertation (MEng)--University of Pretoria, 2012.