Novel Partitioned Coupling Algorithms For Fluid-structure Interaction With Applications To Aeroelasticity

Fluid-structure interaction (FSI) being a challenging topic in computational fluiddynamics arises from a variety of practical engineering, such as wind-structure interaction,flutter and kinetic stability of spacecrafts, liquid slosh in a container and vortex-inducedvibrations of marine risers. Taking FSI into account is thereby of great importance toengeering structures’ safety. Partitioned approaches, which evaluate individual fieldssequentially, are often employed for the numerical solution of FSI due to the complexity andsuper large-scale computing of practical applications. Although traditional partitioned solutionapproaches are economical, they fail to lead to the synchronous computation of the coupledFSI system. The asynchrony caused by partitioned techniques gives arise to the well-knowntime lag effect in partitioned explicit coupling methods and possibly leads to convergencedifficulty in partitioned implicit coupling methods. The relevant computations may besubjected to the undesired numerical instability. As a consequence, it is advisable to estabilishnew interface conditions and the associated partitioned coupling algorithms from theacademic significance and engineering practice’s point of view. The main purpose of thepresent dissertation is to provide an effective way to eliminate the aforementioned problemsin partitioned FSI calculations, and the potential for meeting the practical needs.In order to eliminate the asynchrony in partitioned approaches, to enhance the robustnessof coupling schemes and to improve the accuracy of FSI computations, the combinedinterface boundary condition (CIBC) method is applied to the fluid-strucutre interface. TheCIBC method can rectify the missing information on the interface and contributes to buildingnew partitioned coupling schemes. However, the structure is assumed to be deformable in theoriginal CIBC method, and the traction rate that appears explicitly in the traction correctionterm is estimated based on the solution of the structural subsystem. Two major limitations of the CIBC method therefore are identified:(1) the structural traction is required before it iscorrected; and (2) the method fails to solve fluid-rigid body interaction since a rigid bodydoes not produces internal stress. To this end, the modified CIBC method is developed viamathematical manipulation. The developed method is validated by various numerical tests.The main work and innovation in the present dissertation focus on the following parts.1. New interface conditions, namely, the modified CIBC formulae are developed tofacilitate the building of hybrid interface coupling conditions. A new CIBC formulation ismathematically derived via a simple first order ordinary differential equation. The developedmethod where the structural traction completely disappears before it is corrected can beapplied to the fluid-rigid body interaction. A new coupling parameter which considers theeffect of time step is adopted in order to adjust the effect of interfacial corrections. The rangeof this parameter is suggested. The interfacial displacement continuity due to CIBC correctionis well maintained.2. Novel partitioned solution techniques for FSI are proposed. Several partitionedsolution techniques are presented based on the modified CIBC method, involving the explicit,semi-implicit and implicit coupling methods. The semi-implicit coupling algorithm is inspiredby the characteristic-based split (CBS) fluid solver, and thus it is called a CBS-basedpartitioned semi-implicit coupling strategy. The present CBS-based semi-implicit couplingapproach represents the merits of both explicit and implicit methods, hence rendering low costwithout compromising stability. The subiterations per time step are achieved by the classicalfixed-point iteration with Aitken acceleration technique. The difference between partitionedsubiterative coupling methods and the sequence of the subsystems’ solutions are discussed. Apartitioned implicit coupling algorithm which is more applicable to the CIBC method isproposed. The above work provides stable and effective partitioned coupling schemes fornumerical solutions of FSI, and is of academic importance to the development of novelpartitioned methods.3. The improvements of components of the coupled FSI system are achieved. Therigid-body dynamics is evaluated by a composite implicit time integration method that canaccommodate a larger time step. To attain a more accurate solution, the so-called gradientsmoothing technique in conjunction with Newton-Raphson iterations is used to solve thefinite deformation of an elastic body. A simple and efficient moving submesh approach isemployed for the dynamic mesh with the aid of the ortho-semi-torisonal spring analogy method, reducing the computational cost remarkably and requiring no smoothing for thecoordinates of the dynamic mesh. The resulting quasi-static equilibrium equations of thespring analogy method are solved by a simple successive over relaxation technique instead ofthe preconditioned conjugate gradient solver. To satisfy geometric conservation law, a masssource term is implanted into the CBS scheme on the moving mesh with permission ofarbitrary scheme of mesh velocity. The above work presents the enhancements of thenumerical solutions of FSI.4. The modified CIBC method is applied to various flow-induced vibrations of abluff body to reveal the structure’s responses and the relevant features. The flow-inducedvibrations of a circular, a square and a rectangular cylinder are studied in detail, involvingone-degree-of-freedom translational and torsional motions, and two-degree-of-freedommotions. In all numerical examples, a few numerical details are carefully analyzed and theeffect of Reynolds number is studied in detail. The cylinder response, aerodynamicparameters and flow features are also discussed when varying Reynolds number. Theresponses and flows’ characteristics are hence realized, providing reference for numericalcomputations and engineering projects.This dissertation is devoted to developing several efficient and stable partitioned couplingalgorithms and improvements of individual components in the whole FSI system. Allexamples considered herein are implemented by our FORTRAN codes. The present researchfindings will benefit to disciplines such as civil engineering, ocean engineering, aerospaceengineering and so on, and are of academic significance to progress the knowledge of FSI andits numerical solution.