Lagrangian-Eulerian finite element formulation for incompressible viscous flows

Hughes, Thomas J.R.; Liu, Wing Kam; Zimmermann, Thomas

doi:10.1016/0045-7825(81)90049-9

Cited by 1,354 publications

(715 citation statements)

References 4 publications

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“…The thermal equation is derived from the energy balance equation and includes conduction-advection in three directions. We do not use s-coordinates [Pattyn, 2003] but rely on the Arbitrary Lagrangian-Eulerian (ALE) method [Hughes et al, 1981;Donea et al, 2004]. The mesh velocity, w, is therefore included in the equation to account for mesh displacements:…”

Section: Thermal Modelmentioning

confidence: 99%

Dynamically and Observationally Constrained Estimates of Water-Mass Distributions and Ages in the Global Ocean

DeVries

Primeau

2011

Journal of Physical Oceanography

180

202

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[1] Ice flow models used to project the mass balance of ice sheets in Greenland and Antarctica usually rely on the Shallow Ice Approximation (SIA) and the Shallow-Shelf Approximation (SSA), sometimes combined into so-called "hybrid" models. Such models, while computationally efficient, are based on a simplified set of physical assumptions about the mechanical regime of the ice flow, which does not uniformly apply everywhere on the ice sheet/ice shelf system, especially near grounding lines, where rapid changes are taking place at present. Here, we present a new thermomechanical finite element model of ice flow named ISSM (Ice Sheet System Model) that includes higher-order stresses, high spatial resolution capability and data assimilation techniques to better capture ice dynamics and produce realistic simulations of ice sheet flow at the continental scale. ISSM includes several approximations of the momentum balance equations, ranging from the two-dimensional SSA to the three-dimensional full-Stokes formulation. It also relies on a massively parallelized architecture and state-of-the-art scalable tools. ISSM employs data assimilation techniques, at all levels of approximation of the momentum balance equations, to infer basal drag at the ice-bed interface from satellite radar interferometry-derived observations of ice motion. Following a validation of ISSM with standard benchmarks, we present a demonstration of its capability in the case of the Greenland Ice Sheet. We show ISSM is able to simulate the ice flow of an entire ice sheet realistically at a high spatial resolution, with higher-order physics, thereby providing a pathway for improving projections of ice sheet evolution in a warming climate.Citation: Larour, E., H. Seroussi, M. Morlighem, and E. Rignot (2012), Continental scale, high order, high spatial resolution, ice sheet modeling using the Ice Sheet System Model (ISSM),

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Section: Thermal Modelmentioning

confidence: 99%

Dynamically and Observationally Constrained Estimates of Water-Mass Distributions and Ages in the Global Ocean

DeVries

Primeau

2011

Journal of Physical Oceanography

180

202

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“…As detailed in the work of T.J.R. Hughes et al (1981), this domain is introduced as a third domain additionally to the common material and spatial domains. These domains correspond to the Lagrangian and Eulerian domains, respectively.…”

Section: Arbitrary-lagrangian-eulerian (Ale) Finite Element Methodsmentioning

confidence: 99%

Dynamic responses and damages of water-filled cylindrical shell subjected to explosion impact laterally

Gao

Long

et al. 2014

Lat. Am. j. solids struct.

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An account is given of some principal observations made from a series of experiments in which metal cylindrical shells were subjected to lateral explosion impact by different TNT charge mass and stand-off distance. These cylindrical shells were filled with water in order to identify the main effects produced by the fluid-structure interaction. In comparison, the explosion impact experiments of the empty cylindrical shells were also carried out. The effects of TNT charge mass, stand-off distance, cylindrical shell wall thickness and filled fluid (water) on perforation and deformation of metal cylindrical shells were discussed, which indicated that water increased the wall strength of the cylindrical shells under explosion impact loading, and the buckling deformation and perforation of the cylindrical shell was significantly influenced by the presence of the water; blast-resistant property of the tube under explosive impact loading of 200g TNT charge was much excellent; deformation and damage of empty cylindrical shell were more sensitive to stand-off distance changed. ALE finite element method was employed to simulate the deformations and damages of empty and water-filled cylindrical shells under explosion impact loading. The experimental and computational results are in agreement, showing the validity of the computational scheme in complex fluid-structure interaction problems involving metal materials subjected to explosion impact. The results show that internal pressure of water will increase when subjecting to impact loading, the anti-blast ability of tube structure is significantly enhanced.

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“…The advection phase has been added to the LS-DYNA code extending the range of applications that can be used with the ALE formulation [10,11,12,13]. Current industrial applications include: sloshing involving a 'free surface' [14], and slamming problems [15], which are high velocity impact problems where the target is modeled as a fluid material, thus providing a more realistic representation of the impact event by capturing large deformations.…”

Section: Ale Descriptionmentioning

confidence: 99%

“…An ALE formulation contains both pure Lagrangian and pure Eulerian formulations [10]. The pure Lagrangian description is the approach that: the mesh moves with the material, making it easy to track interfaces and to apply boundary conditions.…”

Section: Ale Descriptionmentioning

confidence: 99%

Transient Response of a Projectile in Gun Launch Simulation Using Lagrangian and Ale Methods

Tabiei¹,

Chowdhury²,

Aquelet³

et al. 2010

The International Journal of Multiphysics

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Lagrangian-Eulerian finite element formulation for incompressible viscous flows

Cited by 1,354 publications

References 4 publications

Dynamically and Observationally Constrained Estimates of Water-Mass Distributions and Ages in the Global Ocean

Dynamically and Observationally Constrained Estimates of Water-Mass Distributions and Ages in the Global Ocean

Dynamic responses and damages of water-filled cylindrical shell subjected to explosion impact laterally

Transient Response of a Projectile in Gun Launch Simulation Using Lagrangian and Ale Methods

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