Equations governing the flow of fluid containing visco-hyperelastic particles are developed in an Eulerian framework. The novel feature introduced here is to write an evolution equation for the strain. It is envisioned that this will simplify numerical codes which typically compute the strain on Lagrangian meshes moving through Eulerian meshes. Existence results for the flow of linear visco-hyp...

In this work, we present a Fully Eulerian framework for fluid-structure interaction (fsi) problems coupling the incompressible Navier-Stokes equations with a hyperelastic solid. The Fully Eulerian framework is a monolithic implicit variational formulation for the coupled problem. In contrast to the well-established Arbitrary Lagrangian Eulerian (ALE) coordinates, the Fully Eulerian framework fo...

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian represe...

In this note we explain how to derive an asymptotic formula for solutions of the 2d gravity water waves system expressed in Eulerian coordinates, using some of the bounds obtained by the authors in [IPu13]. The main ingredients of the proof are: 1) the uniform estimates for the Fourier transform of the profile of solutions obtained in [IPu13], 2) a refined linear estimate for the propagator exp...

Under a generalized coordinate transformation with arbitrary grid velocity, the gas-kinetic BGK equation is reformulated in a moving frame of reference. Then, a unified conservative gas-kinetic scheme is developed for the viscous flow computation in the moving grid system in the Eulerian space. Due to the coupling between the grid velocity and the overall solution algorithm, the Eulerian and La...

This paper presents a novel hybrid particle-grid method that tightly couples Lagrangian particle approach with Eulerian grid approach to simulate multi-scale diffuse materials varying from disperse droplets to dissipating spray and their natural mixture and transition, originated from a violent (high-speed) liquid stream. Despite the fact that Lagrangian particles are widely employed for repres...

This study uses a global ocean eddy-permitting climate model to explore the export of abyssal water from the Southern Ocean and its sensitivity to projected twenty-first-century poleward-intensifying Southern Oceanwind stress. The abyssal flow pathways and transport are investigated using a combination of Lagrangian and Eulerian techniques. In an Eulerian format, the equatorand poleward flows w...

Simultaneous measurements of turbulent vertical velocity fluctuations at a height of 300 ft. measured by means of a fixed anemometer, small floating balloons, and airplane gust equipment at Brookhaven are presented. The resulting Eulerian (fixed anemometer) turbulence energy mectra are similar to the Lagrangian (balloon) spectra but "-with a displacement toward higher frequencies. The term Eule...