A Compatible, Energy and Symmetry Preserving Lagrangian Hydrodynamics Algorithm in Three-Dimensional Cartesian Geometry

Caramana, E.J.; Rousculp, C. L.; Burton, Donald E.

doi:10.1006/jcph.1999.6368

Cited by 65 publications

(51 citation statements)

References 13 publications

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“…This last equation has been previously derived and utilized in [10,11] in order to construct compatible hydrodynamics algorithms using the method of Support Operators.…”

Section: Commentmentioning

confidence: 99%

“…Here, the time derivative d dt V c is computed by using (11). Let C V be a strictly positive coefficient, C V ∈]0, 1[.…”

Section: Criterion On the Variation Of Volumementioning

confidence: 99%

“…This is a well known difficult test case that enables to validate the robustness of a Lagrangian scheme when the mesh is not aligned with the fluid flow. Here, we consider the three-dimensional extension of this test that has been proposed in [11]. The computational domain is the volume defined by …”

Section: D Saltzmann Problemmentioning

confidence: 99%

“…Finally, the discretization of artificial viscosity has been considerably improved: first by introducing formulations for 1 multidimensional shock wave computations [9] and then by deriving a tensorial artificial viscosity with a mimetic finite difference discretization [7]. The three-dimensional extension of the SGH discretization can be found in [11] and also in [6].…”

Section: Introductionmentioning

confidence: 99%

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Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics

Maire

Nkonga

2009

Journal of Computational Physics

112

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This work presents a multidimensional cell-centered unstructured finite volume scheme for the solution of multimaterial compressible fluid flows written in the Lagrangian formalism. This formulation is considered in the Arbitrary-Lagrangian-Eulerian (ALE) framework with the constraint that the mesh and the fluid velocity coincide. The link between the vertex velocity and the fluid motion is obtained by a formulation of the momentum conservation on a class of multi-scale encased volumes around mesh vertices. The vertex velocity is derived with a nodal Riemann solver constructed in such a way that the mesh motion and the face fluxes are compatible. Finally, the resulting scheme conserves both momentum and total energy and, it satisfies a semi-discrete entropy inequality. The numerical results obtained for some classical 2D and 3D hydrodynamic test cases show the robustness and the accuracy of the proposed algorithm.

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“…This last equation has been previously derived and utilized in [10,11] in order to construct compatible hydrodynamics algorithms using the method of Support Operators.…”

Section: Commentmentioning

confidence: 99%

“…Here, the time derivative d dt V c is computed by using (11). Let C V be a strictly positive coefficient, C V ∈]0, 1[.…”

Section: Criterion On the Variation Of Volumementioning

confidence: 99%

Section: D Saltzmann Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics

Maire

Nkonga

2009

Journal of Computational Physics

112

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“…This is a staggered grid [5,6] spatial discretization. A standard lumped mass finite element (or finite difference) discretization of this system of equations yields the difference stencil…”

Section: Vonneumann Stability Analysismentioning

confidence: 99%

Algorithmic properties of the midpoint predictor-corrector time integrator.

Rider¹,

Love²,

Scovazzi³

2009

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Algorithmic properties of the midpoint predictor-corrector time integration algorithm are examined. In the case of a finite number of iterations, the errors in angular momentum conservation and incremental objectivity are controlled by the number of iterations performed. Exact angular momentum conservation and exact incremental objectivity are achieved in the limit of an infinite number of iterations. A complete stability and dispersion analysis of the linearized algorithm is detailed. The main observation is that stability depends critically on the number of iterations performed.

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3D staggered Lagrangian hydrodynamics scheme with cell‐centered Riemann solver‐based artificial viscosity

Loubère

Maire

Váchal

2012

Numerical Methods in Fluids

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A Compatible, Energy and Symmetry Preserving Lagrangian Hydrodynamics Algorithm in Three-Dimensional Cartesian Geometry

Cited by 65 publications

References 13 publications

Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics

Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics

Algorithmic properties of the midpoint predictor-corrector time integrator.

3D staggered Lagrangian hydrodynamics scheme with cell‐centered Riemann solver‐based artificial viscosity

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