Lagrangian Gas Dynamics in Two Dimensions and Lagrangian systems

Després, Bruno; Mazeran, Constant

doi:10.1007/s00205-005-0375-4

Cited by 209 publications

(255 citation statements)

References 22 publications

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“…In order to write these equations in a full Lagrangian way, one has to express the gradient and divergence operators with Lagrangian coordinates using the map M t . For such an approach, the reader should referred to [15], [20] and [9].…”

Section: Derivation Of the Euler Equations In The Lagrangian Formalismmentioning

confidence: 99%

A second‐order cell‐centered Lagrangian scheme for two‐dimensional compressible flow problems

Maire

Breil

2007

Numerical Methods in Fluids

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We present a new Lagrangian cell-centered scheme for two-dimensional compressible flows. The primary variables in this new scheme are cell-centered, i.e., density, momentum and total energy are defined by their mean values in the cells. The vertex velocities and the numerical fluxes through the cell interfaces are not computed independently contrary to standard approaches but are evaluated in a consistent manner due to an original solver located at the nodes. The main new features of the algorithm is the introduction of four pressures on each edge, two for each node on each side of the edge. This extra degree of freedom, allows us to construct a nodal solver which fulfills two properties. First, the conservation of momentum and total energy is ensured. Second, a semi-discrete entropy inequality is provided. In the case of a one-dimensional flow, the solver reduces to the classical Godunov acoustic solver: it can be considered as its two-dimensional generalization. Many numerical tests are presented. They are representative test cases for compressible flows and demonstrate the robustness and the accuracy of this new solver.

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Section: Derivation Of the Euler Equations In The Lagrangian Formalismmentioning

confidence: 99%

A second‐order cell‐centered Lagrangian scheme for two‐dimensional compressible flow problems

Maire

Breil

2007

Numerical Methods in Fluids

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“…In this article, we were interested in adapting a new cell centered Lagrangian method for gas dynamics [5] to the problem of the free fall of a droplet inside a 2D glass (filled with air). In this experiment, major deformation problems arise.…”

Section: Resultsmentioning

confidence: 99%

“…The numerical used for the Lagrangian step of the method is based on some recent works [4,5]. The schemes are Lagrangian which means that the mesh is moving at the fluid pace.…”

Section: The Basic 2d Well-balanced Lagrangian Schemementioning

confidence: 99%

“…The basic algorithm is composed of (3)(4)(5)(6). The equations for the nodal j r l j,r−1 n j,r−1 l j,r+1 n j,r+1 r + 1 r − 1 l j,r n j,r Figure 2.…”

Section: The Basic 2d Well-balanced Lagrangian Schemementioning

confidence: 99%

“…Our idea is twofold. First, to use the newly developed cell centered Lagrangian scheme [4,5] (which has been used to compute Figure 1; actually any other Lagrangian cell centered scheme, such as in [10], could be used instead) and to combine this scheme with 2D algorithms which are known to be efficient for the treatment of large mesh deformations. These algorithms consist in a swap procedure based on the empty ball criterion (or Delaunay criterion).…”

Section: Introductionmentioning

confidence: 99%

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Lagrangian method enhanced with edge swapping for the free fall and contact problem

et al. 2008

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Abstract. We discuss various algorithms that one can use in conjunction with Lagrangian methods for the treatment of important deformation of the mesh. We develop a new contact algorithm. The free fall of a droplet of fluid in a light gas serves to illustrate the potentialities of these techniques.Résumé. Nousétudions un problème modèle de chute libre d'une goutte de fluide dans de l'airà l'aide de méthodes numériques lagrangiennes. Nous développons etétudions un nouvel algorithme de contact qui permet (numériquement)à la goutte de toucher le sol.

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Compressible flow equations based on moving coordinates determined by the wave speed

Chen

Gao

2006

Numerical Methods in Fluids

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SUMMARYIn this paper, we consider moving coordinates with a speed determined by the wave speed. This allows us to move the coordinates at the speed of contact discontinuities, expansion fans, or other wave structures. While recognizing that the Lagrangian coordinates, which can well resolve the sliplines, behave badly for expansion waves, we demonstrate that a coordinate system moving at the characteristic speed of the expansion fan behaves much better for expansion waves. Moreover, the new coordinate system allows one to well capture the shock wave, the slipline and the expansion waves at the same time.

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Lagrangian Gas Dynamics in Two Dimensions and Lagrangian systems

Cited by 209 publications

References 22 publications

A second‐order cell‐centered Lagrangian scheme for two‐dimensional compressible flow problems

A second‐order cell‐centered Lagrangian scheme for two‐dimensional compressible flow problems

Lagrangian method enhanced with edge swapping for the free fall and contact problem

Compressible flow equations based on moving coordinates determined by the wave speed

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