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The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses…
We study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium. The free fluid is governed by the Stokes equations, while the flow in the…
We consider the relationship between Eulerian modal decompositions and Lagrangian coherent structures (LCSs). The model sensitivity framework developed by Kasz\'as and Haller (2020) is used to express data-driven modal representations of…
We present a systematic study of capillary filling for a binary fluid by using a mesoscopic lattice Boltzmann model for immiscible fluids describing a diffusive interface moving at a given contact angle with respect to the walls. The…
We describe in detail a recently proposed lattice-Boltzmann model for simulating flows with multiple phases and components. In particular, the focus is on the modeling of one-component fluid systems which obey non-ideal gas equations of…
A numerical method is presented to simulate gas-liquid-solid flows with bubble-particle interaction, including particle collision, sliding, and attachment. Gas-liquid flows are simulated in an Eulerian framework using a volume-of-fluid…
The immersed boundary (IB) method is a mathematical and numerical framework for problems of fluid-structure interaction, treating the particular case in which an elastic structure is immersed in a viscous incompressible fluid. The IB…
This study examines the stability of a flexible material interface between two fluids of the same viscosity in interaction with a free surface. When the layers are motionless, we provide evidence for the onset of a novel instability by…
A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a BGK collision operator using the lattice Boltzmann method to simulate binary fluid…
We formulate and analyze interior penalty discontinuous Galerkin methods for coupled elliptic PDEs modeling excitable tissue, represented by intracellular and extracellular domains sharing a common interface. The PDEs are coupled through a…
The application of modern topology optimization techniques to single physics systems has seen great advances in the last three decades. However, the application of these tools to sophisticated multiphysics systems such as fluid-structure…
Stimulated by experimental evidence in the field of solution--born thin films, we study the morphology formation in a three state lattice system subjected to the evaporation of one component. The practical problem that we address is the…
We investigate a relativistic adaptation of the Lattice Boltzmann Method that reproduces the equations of motion for a turbulent, two-dimensional, massless hydrodynamic system. The classical Lattice Boltzmann Method and its extension to…
We develop our existing two-dimensional lattice-gas model to simulate the flow of single-phase, binary-immiscible and ternary-amphiphilic fluids. This involves the inclusion of fixed obstacles on the lattice, together with the inclusion of…
The deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barthes-Biesel, J. M. Rallison, The Time-Dependent Deformation of a Capsule Freely…
We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a Lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects…
A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal…
We consider a computational model for complex-fluid-solid interaction based on a diffuse-interface model for the complex fluid and a hyperelastic-material model for the solid. The diffuse-interface complex-fluid model is described by the…
Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In the real-life applications like blood flow, there is often an additional complexity of vorticity being…
This work focuses on the development and analysis of a partitioned numerical method for moving domain, fluid-structure interaction problems. We model the fluid using incompressible Navier-Stokes equations, and the structure using linear…