Arbitrary Lagrangian–Eulerian method for Navier–Stokes equations with moving boundaries

Duarte, Fabián; Gormaz, Raúl; Natesan, Srinivasan

doi:10.1016/j.cma.2004.05.003

Cited by 120 publications

(105 citation statements)

References 16 publications

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“…As far as the numerical solution of such fluid-solid interaction problems is concerned, several different approaches have been introduced in the literature, based on ALE formulations [7,17,23,24], fictitious domain technique [13], penalty method [20] or Lagrange-Galerkin method [29], but only a few actually received a rigorous analysis of their properties. On this very topic, let us mention the paper of Grandmont et al [15] for proofs of convergence of time decoupling algorithms used to solve an ALE formulation of a one-dimensional fluid-structure interaction problem.…”

Section: S(ζ(t)θ(t))mentioning

confidence: 99%

“…While the Lagrange-Galerkin technique has been used for years for the numerical treatment of convection-diffusion equations like the Navier-Stokes equations (see for instance [1,26,31]), it was more recently introduced in the context of ALE formulations of free surface or two-fluid flow problems [7,12,22] and fluid-structure interaction problems [23,24].…”

Section: Introductionmentioning

confidence: 99%

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Convergence of a Lagrange-Galerkin method for a fluid-rigid body system in ALE formulation

Legendre¹,

Takahashi²

2008

ESAIM: M2AN

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Section: S(ζ(t)θ(t))mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Convergence of a Lagrange-Galerkin method for a fluid-rigid body system in ALE formulation

Legendre¹,

Takahashi²

2008

ESAIM: M2AN

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“…The geometry of the outer boundary will move with the velocity at boundary. The tracking of the moving boundary succeed by using Arbitrary Lagrangian-Eulerian (ALE) method [14]. The heat comes from the oven into the glass at outer boundary via the radiation.…”

Section: Computational Model Of Glass Forming Processmentioning

confidence: 99%

A Concept for Sensitivity Analysis and Parameter Calibration of Coupled Nonlinear Pdes and Its Application to an Industrial Glass Forming Model

Janya-anurak¹,

Bernard²,

Beyerer³

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. Many industrial and environmental processes 702Chettapong Janya-anurak, Thomas Bernard and Jürgen Beyerer INTRODUCTIONNowadays the computer simulation based on mathematical model is commonly applied in every branch of natural science and engineering disciplines. Simulations are essential tools for engineers to analysis, design and control technical processes. Many industrial and environmental processes are characterized as complex spatio-temporal systems. By using physical laws, the systems can be described mathematically with Partial Differential Equations (PDEs).In practice the modeling of the real process often leads to nonlinear coupled PDEs. Such models are often highly complex and their relationships between model inputs, model output and parameters may be poorly understood. Moreover, due to incomplete knowledge on underlying physics, simplifying assumptions or inevitable intrinsic variability, the solutions of physics-based models commonly differ from the real measurements.These problems are widely recognized in the scientific community and have also led the uncertainty quantification (UQ) framework to constitute an active research area recently. Uncertainty Quantification covers a wide range of topics. The relevant issues are, for example, propagation of uncertainty, sensitivity analysis and inverse problem, which are mainly employed through this paper.Under the uncertainty quantification framework, uncertainties in models are quantified using different mathematical tools. Expressing the uncertainties with a probabilistic description seems to be the one mostly chosen in practice. The stochastic approach of uncertainty modeling is achieved by representing uncertainties in the models as random variables, stochastic processes or random fields. However, solving coupled nonlinear PDEs with random variables requires generally extensive computational effort.The generalized Polynomial Chaos has been proposed on the last few years as an efficient methodology to computing in uncertainty quantification framework. The gPC is the extension of the original Polynomial Chaos expansion (PCE), proposed by Wiener in 1938 [1]. The original Wiener's Polynomial Chaos employs Hermite polynomial to represent the Gaussian random processes. The gPC extend the PCE toward some parametric statistical non-Gaussian distribution, based on the Askey scheme of orthogonal polynomials [2].Besides many academic examples have proven the potential of gPC, for example, the uncertainties propagation in PDE [3], calculation of Sobols' Indices for the sensitivity analysis [4] [9]and Bayesian inference in inverse problem [5], the application of gPC are found in a variety of areas, such as fluid dynamic, stricture-flow interactions, material deformations, internal combustion engine and biological problems.In this paper, we propose a concept for sensitivity analysis and parameter calibration of coupled nonlinear PDEs based on gPC-approximation. From user defined parameter uncertainties, the system responses are expanded with Polynomial Cha...

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“…In particular, the distribution of the grid points along the free surface may deteriorate over time, which may ultimately result in severe loss of accuracy (or even breakdown of the simulation). This latter issue may be dealt with in various ways, e.g., through remeshing or other mesh update strategies [11,4]. However, the temporal accuracy will typically suffer using such a strategy.…”

Section: Introductionmentioning

confidence: 99%

“…One could also imagine enforcing the kinematic condition together with a tangential component of the domain velocity in such a way that the integration of the total domain velocity would: (i) result in an accurate representation of the free surface; and (ii) maintain a good distribution of the grid points along the surface [4,2]. An obvious challenge with this approach is how to define the overall domain velocity in such a way that not only good spatial accuracy is achieved (with no need for remeshing), but in a way that will also ensure good temporal accuracy (better than first order).…”

Section: Introductionmentioning

confidence: 99%

Accurate interface-tracking for arbitrary Lagrangian–Eulerian schemes

Bjøntegaard

Rønquist

2009

Journal of Computational Physics

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We present a new method for tracking an interface immersed in a given velocity field. The method is particularly relevant to the simulation of unsteady free surface problems using the arbitrary Lagrangian-Eulerian (ALE) framework. The new method has been constructed with two goals in mind: (i) to be able to accurately follow the interface; and (ii) to maintain a good point distribution for the grid points along the interface. The method combines information from a pure Lagrangian approach with information from an ALE approach. No integration backwards in time is needed; instead, the new method relies of the solution of several pure convection problems along the interface in order to obtain the relevant information. The new method offers flexibility in terms of how an "optimal" point distribution should be defined. We have been able to verify first, second, and third order temporal accuracy for the new method by solving two-dimensional model problems with known solutions.

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Arbitrary Lagrangian–Eulerian method for Navier–Stokes equations with moving boundaries

Cited by 120 publications

References 16 publications

Convergence of a Lagrange-Galerkin method for a fluid-rigid body system in ALE formulation

Convergence of a Lagrange-Galerkin method for a fluid-rigid body system in ALE formulation

A Concept for Sensitivity Analysis and Parameter Calibration of Coupled Nonlinear Pdes and Its Application to an Industrial Glass Forming Model

Accurate interface-tracking for arbitrary Lagrangian–Eulerian schemes

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