Related papers: An Immersed Interface Method for Incompressible Fl…
We present a numerical approximation of Darcy's flow through a porous medium that incorporates networks of fractures with non empty intersection. Our scheme employs PolyDG methods, i.e. discontinuous Galerkin methods on general polygonal…
We perform high-order simulations of two-phase flows in capillaries, with and without evaporation. Since a sharp-interface model is used, singularities can arise at the three-phase contact line, where the fluid-fluid interface interacts…
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…
The immersed boundary (IB) method is an approach to fluid-structure interaction that uses Lagrangian variables to describe the structure and Eulerian variables to describe the fluid. Explicit time stepping schemes for the IB method require…
Immersed boundary methods are extensively used for simulations of dynamic solid objects interacting with fluids due to their computational efficiency and modelling flexibility compared to body-fitted grid methods. However, thin geometries,…
In this paper we present an immersed weak Galerkin method for solving second-order elliptic interface problems on polygonal meshes, where the meshes do not need to be aligned with the interface. The discrete space consists of constants on…
An immersed interface-lattice Boltzmann method (II-LBM) is developed for modelling fluid-structure systems. The key element of this approach is the determination of the jump conditions that are satisfied by the distribution functions within…
This paper develops and analyzes two fully discrete interior penalty discontinuous Galerkin (IP-DG) methods for the Allen-Cahn equation, which is a nonlinear singular perturbation of the heat equation and originally arises from phase…
Our paper proposes an innovative approach for modeling Fluid-Structure Interaction (FSI). Our method combines both traditional monolithic and partitioned approaches, creating a hybrid solution that facilitates FSI. At each time iteration,…
The aim of this paper is to provide a survey of the state of the art in the finite element approach to the Immersed Boundary Method (FE-IBM) which has been investigated by the authors during the last decade. In a unified setting, we present…
The interfacial diffusion associated with finite volume method (FVM) discretizations of multiphase flows creates the need for an interface sharpening mechanism. Such solutions for structured quadrilateral grids are well documented, but…
The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines,…
We introduce fluctuating hydrodynamics approaches on surfaces for capturing the drift-diffusion dynamics of particles and microstructures immersed within curved fluid interfaces of spherical shape. We take into account the interfacial…
We present a new high-order accurate Lagrangian discontinuous Galerkin (DG) hydrodynamic method to simulate material dynamics (for e.g., gasses, fluids, and solids) with up to fourth-order accuracy on cubic meshes. The variables, such as…
We present an immersed boundary projection method formulated in a body-fixed frame of reference for flow-structure interaction (FSI) problems involving rigid bodies with complex geometries. The body-fixed formulation is aimed at maximizing…
A numerical tool relying on sharp Immersed Boundary Method (IBM) is developed for the analysis of aerospace applications. The method, which is conceived for application using segregated solvers relying on implicit time discretization, uses…
In recent years, high-order discontinuous Galerkin (DG) methods have emerged as an attractive approach for numerical simulations of compressible flows. This paper presents an overview of the recent development of DG methods for compressible…
Computational modeling and simulation of fluid-structure interactions constitute a fundamental cornerstone for advancing aerospace engineering endeavors. This paper addresses the notion and implementation of the immersed boundary method for…
This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…
We present a robust immersed boundary (IB) method for high density ratio multiphase flows that is capable of modeling complex wave-structure interaction (WSI) problems arising in marine and coastal engineering applications. The IB/WSI…