Arbitrary<scp>L</scp>agrangian–<scp>E</scp>ulerian Methods

Donéa, J.; Huerta, Antonio; Ponthot, Jean‐Philippe; Rodrï¿1⁄2ï¿1⁄2guez-Ferran, A.

doi:10.1002/0470091355.ecm009

Cited by 580 publications

(479 citation statements)

References 85 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

183

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

183

202

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“…It is commonly accepted to combine the best feature of pure Lagrangian framework to track the free surface and pure Eulerian framework to handle large distortion in a mesh. The combined FSI formulations are described by the following equations based on the formulations in [9]. Let Ω f be the fluid domain bounded by the boundary ∂Ω f , then velocity vector of fluid v and scalar field pressure in fluid p are given by:…”

Section: Fsi Formulationmentioning

confidence: 99%

“…The structure domain is modelled using St. Venant Kirchoff (STVK) material model [8]. Since structure usually resides in Lagrangian framework while fluid in Eulerian framework, the conventional ALE framework to describe both structure and fluid formulation in one common framework is used [9]. The ALE framework allows the node of the elements to move in normal Lagrangian framework or held fixed in Eulerian manner.…”

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confidence: 99%

Finite Element Method for Fluid Structure Interaction with hp-Adaptivity

Abas¹,

Abdul-Rahman²

2013

IJCTE

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Abstract-Recent advances in computational studies of fluid flows with structural interactions suggest that significant contributions have been made towards reliable solutions to the problem. Achieving accurate solutions however remains a considerable task since enormous amount of computer time and memory are usually needed. This applies particularly to a partitioned approach in which structure and fluid are solved separately. This paper attempts to solve fluid-structure interaction (FSI) problems with an hp-adaptive finite element method (hp-FEM). The FSI problem is formulated based on a partitioned approach and Arbitrary Lagrangian-Eulerian (ALE) descriptions for the incompressible fluid and structure domains. The hp-adaptivity is implemented with an a posteriori error estimator and adaptation to minimize error in energy norm. The automatic mesh adaptation over the triangular mesh is achieved with red-green-blue refinement technique. A strategy for mesh refinement to occur at prescribed key points is used for effective mesh adaptivity. The hp-adaptive approach is assessed with traditional uniform mesh refinement and also an h-adaptive method on a benchmark test case. From the error convergence, the hp-adaptive method is shown to be a viable approach in acquiring accurate solution of a partitioned-based FSI analysis without significant compromise in computational time and memory. It is also found that the convergence of solution in fluid and structure domains is considerably sensitive to the aspect ratios of triangular elements.Index Terms-Fluid structure interaction, finite element analysis, hp-FEM, a posteriori error estimates. I. INTRODUCTIONAnalysis of fluid flows that are being impeded by an elastic structure poses a particularly challenging task as it is a complex multiphysics problem in which fluid and structure are mutually coupled along a shared boundary. The past few years have seen growing interests in the analysis of fluid-structure interaction (FSI) problems that arise in interdisciplinary fields spanning from biomechanical to microsystems applications [1], [2]. Hence, accurate tools that provide deep understanding of the phenomenon are always of significant interests. Despite considerable advances in the computational analysis of the FSI problems, achieving reasonable accuracy of the solution without excessive computational resources remains an open challenge. This paper attempts to solve the fluid-structure interaction problem with an hp-adaptive finite element method (hp-FEM), in which a careful decision in local mesh refinement (h) combined with increase in polynomial order Manuscript received October 5, 2012; revised January 17, 2013. This work was supported in part by the Malaysia Ministry of Higher Education under its fellowships scheme.The authors are with the School of Mechanical Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia (e-mail: aizat_abas@ yahoo.com; arahman@ eng.usm.my).(p) based on an error indicator is expected to result in highly accurate solution. I...

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“…For a general review of the two computational approaches, see [5]. A popular method to address large deformations, the Arbitrary Lagrangian-Eulerian technique, employs a combination in order to seek the best of both worlds, see e.g., [11,13,23].…”

Section: Introductionmentioning

confidence: 99%

Novel basin modelling concept for simulating deformation from mechanical compaction using level sets

et al. 2017

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As sedimentation progresses in the formation and evolution of a depositional geologic basin, the rock strata are subject to various stresses. With increasing lithostatic pressure, compressional forces act to compact the porous rock matrix, leading to overpressure buildup, changes in the fluid pore pressure and fluid flow. In the context of petroleum systems modelling, the present study concerns the geometry changes that a compacting basin experiences subject to deposition. The purpose is to track the positions of the rock layer interfaces as compaction occurs. To handle the challenge of potentially large geometry deformations, a new modelling concept is proposed that couples the pore pressure equation with a level set method to determine the movement of lithostratigraphic interfaces. The level set method propagates an interface according to a prescribed speed. The coupling term for the pore pressure and level-set equations consists of this speed function, which is dependent on the compaction law. The two primary features of this approach are the simplicity of the grid and the flexibility of the speed function. A first evaluation of the model concept is presented based on an implementation for one spatial dimension accounting for vertical effective stress. Isothermal conditions with a constant fluid density and viscosity were assumed. The accuracy of the implemented numerical solution for the case of a single stratigraphic unit with a linear compaction law was compared to the available analytical solution [38]. The multi-layer setup and the nonlinear case were tested for plausibility.

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ArbitraryLagrangian–Eulerian Methods

Cited by 580 publications

References 85 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

Finite Element Method for Fluid Structure Interaction with hp-Adaptivity

Novel basin modelling concept for simulating deformation from mechanical compaction using level sets

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