A cell-centered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension

Carré, Gilles; Pino, Stéphane Del; Després, Bruno; Labourasse, Emmanuel

doi:10.1016/j.jcp.2009.04.015

Cited by 157 publications

(208 citation statements)

References 33 publications

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“…This original approach leads to first-order conservative schemes which satisfy a local semi-discrete entropy inequality. The multi-dimensional high-order extension of these schemes are developed in [32,87,83,82].…”

Section: Lagrangian Phasementioning

confidence: 99%

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ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method

Loubère

Maire

Shashkov

et al. 2010

Journal of Computational Physics

186

130

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We present a new reconnection-based Arbitrary Lagrangian Eulerian (ALE) method. The main elements in a standard ALE simulation are an explicit Lagrangian phase in which the solution and grid are updated, a rezoning phase in which a new grid is defined, and a remapping phase in which the Lagrangian solution is transferred (conservatively interpolated) onto the new grid. In standard ALE methods the new mesh from the rezone phase is obtained by moving grid nodes without changing connectivity of the mesh. Such rezone strategy has its limitation due to the fixed topology of the mesh. In our new method we allow connectivity of the mesh to change in rezone phase, which leads to general polygonal mesh and allows to follow Lagrangian features of the mesh much better than for standard ALE methods. Rezone strategy with reconnection is based on using Voronoi tessellation. We demonstrate performance of our new method on series of numerical examples and show it superiority in comparison with standard ALE methods without reconnection.

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Section: Lagrangian Phasementioning

confidence: 99%

“…The numerical methods related to Lagrangian phase of ALE are relatively well developed (for example [19,27,26,17,29,79,28,30,37,31,105,104,106,32,87,15,99,84,85,83]), as well as the remapping phase (being considered as conservative interpolation or advection) [19,89,74,59,81,96,120,46,20,45,93].…”

Section: Introductionmentioning

confidence: 99%

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method

Loubère

Maire

Shashkov

et al. 2010

Journal of Computational Physics

186

130

View full text Add to dashboard Cite

show abstract

“…An extension to the 3D case was given in [5]. For a more detailed and deep understanding of the scheme the reader is invited to go through the above references.…”

Section: The Glace Schemementioning

confidence: 99%

“…The shell implosion test case (see [5]) is defined as follows. The initial domain is the area between the two circles centered in 0 of radius 1 and 0.95.…”

Section: Shell Implosion Test Casementioning

confidence: 99%

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Polynomial Least-Squares reconstruction for semi-Lagrangian Cell-Centered Hydrodynamic Schemes

et al. 2009

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Abstract. In Inertial Confinement Fusion (ICF) simulation, use of Lagrangian hydrodynamic numerical schemes is a cornerstone. It avoids mixing of materials and allows for symmetry preservation in dimension two. Recently, [7] and then [9] proposed an interesting alternative to the historical VNR scheme [15]. These two first order schemes are multidimensional generalizations of the Godunov acoustic solver. Alternatively, a WENO Lagrangian scheme was proposed in [6]. This scheme suffers from non-preservation of symmetries and its velocity computation can be discussed.The aim of this work is to evaluate the later scheme on ICF representative test cases and to derive a polynomial reconstruction that preserves symmetries for the three cell-centered scheme. This reconstruction is inspired by [12]. Since this paper focuses on the approximation of Euler equations, considered test cases are purely hydrodynamic and do not illustrate all difficulties encountered in ICF.We first briefly recall different schemes used for this study. We then explain the Least-Squares ENO reconstruction that we chose for symmetry preservation and describe the limiting strategy. We finally illustrates the presented results by some representative numerical experiments.Résumé. La simulation de Fusion par Confinement Inertiel (FCI) utilise souvent des schémas hydrodynamiques Lagrangiens. Cela permet d'éviter le mélange de matériaux et permet de préserver des symétries en dimension deux. Récemment, des alternatives intéressantes au schéma historique VNR [15] ontété proposées dans [7] puis dans [9]. Parallèlement, un schéma WENO aété proposé dans [6]. Ce schéma ne préserve pas les symétries et le calcul des vitesses peutêtre discuté. L'objectif de ce travail est d'évaluer ce dernier schéma pour des cas tests représentatifs de la FCI et d'écrire une reconstruction polynomiale qui préserve les symétries pour les trois schémasétudiés. Cette reconstruction est inspirée de [12]. Puisqu'on se concentre ici sur la résolution deséquations d'Euler, les cas tests présentés sont purement hydrodynamiques et ne prétendent pas couvrir l'ensemble des difficultés rencontrées en FCI.Nous rappelons d'abord les différents schémas utilisés ici. Nous expliquons ensuite la reconstruction au sens des moindres carrés que nous avons choisie ainsi qu'une stratégie de limitation préservant aussi la symétrie. On illustre finalement les résultats au travers de quelques cas tests représentatifs choisis.

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A unified sub‐cell force‐based discretization for cell‐centered Lagrangian hydrodynamics on polygonal grids

Maire

2011

Numerical Methods in Fluids

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SUMMARYWe develop a general formalism to derive cell-centered Lagrangian scheme, wherein numerical fluxes are expressed in terms of sub-cell force. The general form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete entropy inequality. Sub-cell force and nodal velocity are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. Numerical results demonstrate the accuracy and the robustness of this scheme.

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A cell-centered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension

Cited by 157 publications

References 33 publications

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method

Polynomial Least-Squares reconstruction for semi-Lagrangian Cell-Centered Hydrodynamic Schemes

A unified sub‐cell force‐based discretization for cell‐centered Lagrangian hydrodynamics on polygonal grids

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