Related papers: Lagrangian Covector Fluid with Free Surface
A numerical method for the two-dimensional, incompressible Navier--Stokes equations in vorticity--streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and diffusion terms, thus achieving…
An arbitrary Lagrangian--Eulerian (ALE) finite element method for arbitrarily curved and deforming two-dimensional materials and interfaces is presented here. An ALE theory is developed by endowing the surface with a mesh whose in-plane…
Particle-based methods are a practical tool in computational fluid dynamics, and novel types of methods have been proposed. However, widely developed Lagrangian-type formulations suffer from the nonuniform distribution of particles, which…
Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…
A lagrangian for relativistic fluid systems with matters inside is developed using gauge principle. In the model, the gauge boson represents the fluid field in a form $A_\mu \equiv \epsilon_\mu \phi$, where $\epsilon_\mu$ contains the fluid…
The flow properties at the leading edge of a flat plate represent a singularity to the Blasius laminar boundary layer equations; by applying the Lagrangian approach the leading edge velocity profiles of the laminar boundary layer over a…
In this paper, a class of fully nonlinear flows with nonlinear Neumann type boundary condition is considered. This problem was solved partly by the first author under the assumption that the flow is the parabolic type special Lagrangian…
This paper provides a precise sense in which the time t map for the Euler equations of an ideal fluid in a region in R^n (or a smooth compact n-manifold with boundary) is a Poisson map relative to the Lie-Poisson bracket associated with the…
We propose a model for the coupling between free fluid and a linearized poro-hyperelastic body. In this model, the Brinkman equation is employed for fluid flow in the porous medium, incorporating inertial effects into the fluid dynamics. A…
This paper presents a general and robust method for the fluid-structure interaction of membranes and shells undergoing large displacement and large added-mass effects by coupling an immersed-boundary method with a shell finite-element…
This paper is devoted to the geometric analysis of the incompressible averaged Euler equations on compact Riemannian manifolds with boundary. The equation also coincides with the model for a second-grade non-Newtonian fluid. We study the…
Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…
The Lagrangian approach is natural to study issues of turbulent dispersion and mixing. We propose in this work a general Lagrangian stochastic model including velocity and acceleration as dynamical variables for inhomogeneous turbulent…
We consider two laminar incompressible flows coupled by the continuous law at a fixed interface. We approach the system by one that satisfies a friction Navier law, and we show that when the friction coefficient goes to infinity, the…
We devise a numerical method for passive advection of a surface, such as the interface between two incompressible fluids, across a computational mesh. The method is called isoAdvector, and is developed for general meshes consisting of…
Most biological fluids are viscoelastic, meaning that they have elastic properties in addition to the dissipative properties found in Newtonian fluids. Computational models can help us understand viscoelastic flow, but are often limited in…
To describe complex flow systems accurately, it is in many cases important to account for the properties of fluid flows on a microscopic scale. In this work, we focus on the description of liquid-vapor flow with a sharp interface between…
We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its…
A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and…
The question at stake in Lagrangian controllability is whether one can move a patch of fluid particles to a target location by means of remote action in a given time interval. In the last two decades, positive results have been obtained…