Related papers: Arbitrary Lagrangian-Eulerian finite element appro…
It is known that the Eulerian and Lagrangian structures of fluid flow can be drastically different; for example, ideal fluid flow can have a trivial (static) Eulerian structure, while displaying chaotic streamlines. Here we show that ideal…
We propose a novel Particle Flow Map (PFM) method to enable accurate long-range advection for incompressible fluid simulation. The foundation of our method is the observation that a particle trajectory generated in a forward simulation…
We consider a sharp interface formulation for an anisotropic multi-phase Mullins-Sekerka problem with kinetic undercooling. The flow is characterized by a cluster of surfaces evolving such that the total surface energy plus a weighted sum…
We study fully discrete linearized Galerkin finite element approximations to a nonlinear gradient flow, applications of which can be found in many areas. Due to the strong nonlinearity of the equation, existing analyses for implicit schemes…
We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points/lines,…
Particle-laden effects in high-speed flows require a coupled Euler and Lagrangian prediction technique with varying fidelity of thermochemical models, depending on the simulation conditions of interest. This requirement makes the…
We review the main features of an unfitted finite element method for interface and fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical…
This article focusses on the analysis of a conforming finite element method for the time-dependent incompressible Navier-Stokes equations. For divergence-free approximations, in a semi-discrete formulation, we prove error estimates for the…
In this paper, we consider numerical approximations of a binary fluid-surfactant phase-field model coupled with the fluid flow, in which the system is highly nonlinear that couples the incompressible Navier-Stokes equations and two…
We consider a fluid-structure interaction problem in the Eulerian, phase-field formulation. The problem is described using the Navier--Stokes equations for a viscous, incompressible fluid, coupled with the incompressible hyperelasticity…
In this paper, we study both convergence and bounded variation properties of a new fully discrete conservative Lagrangian--Eulerian scheme to the entropy solution in the sense of Kruzhkov (scalar case) by using a weak asymptotic analysis.…
This study presents a high-order, space-time coupled arbitrary Lagrangian Eulerian (ALE) compact gas-kinetic scheme (GKS) for the shallow water equations on moving unstructured meshes. The proposed method preserves both the geometric…
This paper studies a model of two-phase flow with an immersed material viscous interface and a finite element method for numerical solution of the resulting system of PDEs. The interaction between the bulk and surface media is characterized…
Some recently proposed approximations to follow the non--linear evolution of collisionless matter perturbations in the universe are reviewed. The first one, called frozen--flow approximation, is an Eulerian method within Newtonian theory,…
We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed…
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and…
We present an arbitrary updated Lagrangian Material Point Method (A-ULMPM) to alleviate issues, such as the cell-crossing instability and numerical fracture, that plague state of the art Eulerian formulations of MPM, while still allowing…
We consider a time-dependent coupled Navier--Stokes/generalized poroelastic flow problem and propose a unified and monolithic finite element discretization based on implicit time stepping. To handle the fluid-structure interface we employ a…
We develop and analyze a B-spline based arbitrary Lagrangian-Eulerian method of fundamental solutions (ALE-MFS) for curvature-driven motion of two-dimensional evolving domains. Boundary points move with the material to track the geometric…
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…