An ALE/embedded boundary method for two-material flow simulations

Zeng, Xianyi; Li, Kangan; Scovazzi, Guglielmo

doi:10.1016/j.camwa.2018.05.002

Cited by 4 publications

(2 citation statements)

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“…Utilising the transformation expressions described in (13), ( 14) and (15), both the global and local ALE conservation equations for mass, linear momentum and total energy, along with their appropriate Rankine-Hugoniot conditions, can be readily obtained.…”

Section: Ale First Order Conservation Equations For Solidsmentioning

confidence: 99%

“…Motivated by the above pros and cons, Arbitrary Lagrangian Eulerian (ALE) based techniques emerge in order to combine the advantages of purely Lagrangian and Eulerian approaches. The basic idea of the ALE formulation [7][8][9][10][11][12][13][14][15] is the use of a referential (fixed) domain for the description of the motion, different from the material domain (Lagrangian description) and the spatial domain (Eulerian description). Specifically, the computational mesh is neither attached to the material nor kept fixed in space.…”

Section: Introductionmentioning

confidence: 99%

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A first‐order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non‐linear solid dynamics

Di Giusto,

Lee,

Gil

et al. 2024

Numerical Meth Engineering

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SummaryThe paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first‐order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in order to disassociate material particles from mesh positions. Using isothermal hyperelasticity as a starting point, mass, linear momentum and total energy conservation equations are written and solved with respect to the reference configuration. In addition, with the purpose of guaranteeing equal order of convergence of strains/stresses and velocities/displacements, the computation of the standard deformation gradient tensor (measured from material to spatial configuration) is obtained via its multiplicative decomposition into two auxiliary deformation gradient tensors, both computed via additional first‐order conservation laws. Crucially, the new ALE conservative formulation will be shown to degenerate elegantly into alternative mixed systems of conservation laws such as Total Lagrangian, Eulerian and Updated Reference Lagrangian. Hyperbolicity of the system of conservation laws will be shown and the accurate wave speed bounds will be presented, the latter critical to ensure stability of explicit time integrators. For spatial discretisation, a vertex‐based Finite Volume method is employed and suitably adapted. To guarantee stability from both the continuum and the semi‐discretisation standpoints, an appropriate numerical interface flux (by means of the Rankine–Hugoniot jump conditions) is carefully designed and presented. Stability is demonstrated via the use of the time variation of the Hamiltonian of the system, seeking to ensure the positive production of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework. Examples will be restricted to the case of isothermal reversible elasticity to demonstrate the potential of the new formulation.

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Section: Ale First Order Conservation Equations For Solidsmentioning

confidence: 99%