Numerical Methods for Fluid-Structure Interaction - A Review

The interactions between incompressible fluid flows and immersed structures are nonlinear multi-physics phenomena that have applications to a wide range of scientific and engineering disciplines. In this article, we review representative numerical-methods based on conforming and non-conforming meshes that are currently available for computing fluid-structure interaction problems, with an emphasis on some of the recent developments in the field. A goal is to categorize the selected methods and assess their accuracy and efficiency. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study in fluid-structure interaction

Electro-deformation of a moving boundary: a drop interface and a lipid bilayer membrane

This dissertation focuses on the deformation of a viscous drop and a vesicle immersed in a (leaky) dielectric fluid under an electric field. A number of mathematical tools, both analytical and numerical, are developed for these investigations. The dissertation is divided into three parts. First, a large-deformation model is developed to capture the equilibrium deformation of a viscous spheroidal drop covered with non-diffusing insoluble surfactant under a uniform direct current (DC) electric field. The large- deformation model predicts the dependence of equilibrium spheroidal drop shape on the permittivity ratio, conductivity ratio, surfactant coverage, and the elasticity number. Results from the model are carefully compared against the small-deformation (quasispherical) analysis, experimental data and numerical simulation results in the literature. Moreover, surfactant effects, such as tip stretching and surface dilution effects, are greatly amplified at large surfactant coverage and high electric capillary number. These effects are well captured by the spheroidal model, but cannot be described in the second-order small-deformation theory. The large-deformation spheroidal model is then extended to study the equilibrium deformation of a giant unilamellar vesicle (GUV) under an alternating current (AC) electric field. The vesicle membrane is modeled as a thin capacitive spheroidal shell and the equilibrium vesicle shape is computed from balancing the mechanical forces between the fluid, the membrane and the imposed electric field. Detailed comparison against both experiments and small-deformation theory shows that the spheroidal model gives better agreement with experiments in terms of the dependence on fluid conductivity ratio, electric field strength and frequency, and vesicle size. Asymptotic analysis is conducted to compute the crossover frequency where a prolate vesicle crosses over to an oblate shape, and comparisons show the spheroidal model gives better agreement with experimental observations. Finally, a numerical scheme based on immersed interface method for two-phase fluids is developed to simulate the time-dependent dynamics of an axisymmetric drop in an electric field. The second-order immersed interface method is applied to solving both the fluid velocity field and the electric field. To date this has not been done before in the literature. Detailed numerical studies on this new numerical scheme shows numerical convergence and good agreement with the large-deformation model. Dynamics of an axisymmetric viscous drop under an electric field is being simulated using this novel numerical code

Numerical Methods for Fluid-Structure Interaction — A Review

The interactions between incompressible fluid flows and immersed struc-tures are nonlinear multi-physics phenomena that have applications to a wide range of scientific and engineering disciplines. In this article, we review representative numerical methods based on conforming and non-conforming meshes that are currently avail-able for computing fluid-structure interaction problems, with an emphasis on some of the recent developments in the field. A goal is to categorize the selected methods and assess their accuracy and efficiency. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study in fluid-structure interactions

Mathematical modeling, immersed boundary simulation, and experimental validation of the fluid flow around the upside-down jellyfish Cassiopea xamachana

The jellyfish has been the subject of extensive research in the areas of ecology, biomechanics, fluid dynamics and engineering. Previous mathematical and experimental studies of the flows generated by jellyfish focused primarily on swimming mechanisms. Recently, the fluid dynamics of feeding from currents generated during swimming has been considered. In this study the benthic lifestyle of the upside- down jellyfish Cassiopea xamachana was capitalized upon to explore the fluid dynamics of feeding uncoupled from swimming. A two-dimensional mathematical model was developed to capture the fundamental characteristics of the motion of the unique concave bell shape. Given the prominence of the oral arm array, this structure was included and modeled as a porous layer that perturbs the flow generated by bell contractions. The immersed boundary method was used to solve the fluid-structure interaction problem. Parameter sweeps were used to explore numerically the effects of changes in pulse dynamics and the properties of the oral arms independently. Velocity fields obtained from live organisms using digital particle image velocimetry were used to validate the numerical simulations of the model. Parameter sweeps were used to explore the effects of scaling and to compare the model to a more traditional bell-only model. The effects of low-velocity background flow, neighboring jellyfish, and synchronous and asynchronous pulsing were also examined. The presence of the prominent porous layer structure in the field of flow increased the flux of new fluid from along the substrate to the bell. A consistent pattern of flow across the porous layer across a wide range of background flow patterns. The numerical simulations showed that pauses between bell expansion and the next contraction altered fluid flow over the bell and through the oral arms. Studies of the effects of neighboring models showed that spacing and relative size of individuals changed flow rates substantially. These substantial changes could explain so-called hitchhiking behavior observed in smaller or weakened jellyfish