ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method. 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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  1. Abgrall, Rémi; Le Mélédo, Élise; Öffner, Philipp: General polytopal (H(\mathrmdiv))-conformal finite elements and their discretisation spaces (2021)
  2. Asuri Mukundan, Anirudh; Ménard, Thibaut; Brändle de Motta, Jorge César; Berlemont, Alain: A 3D moment of fluid method for simulating complex turbulent multiphase flows (2020)
  3. Balsara, Dinshaw S.; Garain, Sudip; Florinski, Vladimir; Boscheri, Walter: An efficient class of WENO schemes with adaptive order for unstructured meshes (2020)
  4. Cheng, Jian; Zhang, Fan; Liu, Tiegang: A discontinuous Galerkin method for the simulation of compressible gas-gas and gas-water two-medium flows (2020)
  5. Dobrev, Veselin; Knupp, Patrick; Kolev, Tzanio; Mittal, Ketan; Rieben, Robert; Tomov, Vladimir: Simulation-driven optimization of high-order meshes in ALE hydrodynamics (2020)
  6. Dumbser, Michael; Fambri, Francesco; Gaburro, Elena; Reinarz, Anne: On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations (2020)
  7. Florez, Sebastian; Alvarado, Karen; Muñoz, Daniel Pino; Bernacki, Marc: A novel highly efficient Lagrangian model for massively multidomain simulation applied to microstructural evolutions (2020)
  8. Guermond, Jean-Luc; Popov, Bojan; Saavedra, Laura: Second-order invariant domain preserving ALE approximation of hyperbolic systems (2020)
  9. Kemm, Friedemann; Gaburro, Elena; Thein, Ferdinand; Dumbser, Michael: A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer-Nunziato model (2020)
  10. Kenamond, Mack; Shashkov, Mikhail: The distribution-based remapping of the nodal mass and momentum between arbitrary meshes for staggered arbitrary Lagrangian-Eulerian hydrodynamics (2020)
  11. Kucharik, Milan; Loubère, Raphaël: High-accurate and robust conservative remapping combining polynomial and hyperbolic tangent reconstructions (2020)
  12. Luttwak, Gabi: Using the SMG scheme to study the Rayleigh-Taylor instability growth in solids (2020)
  13. Milcent, Thomas; Lemoine, Antoine: Moment-of-fluid analytic reconstruction on 3D rectangular hexahedrons (2020)
  14. Schnücke, Gero; Krais, Nico; Bolemann, Thomas; Gassner, Gregor J.: Entropy stable discontinuous Galerkin schemes on moving meshes for hyperbolic conservation laws (2020)
  15. Zhang, Chao; Menshov, Igor: Eulerian model for simulating multi-fluid flows with an arbitrary number of immiscible compressible components (2020)
  16. Zhang, Chao; Menshov, Igor: An interface-regularizing model for compressible three-fluid flows with interfacial tensions (2020)
  17. Grove, John W.: Some comments on thermodynamic consistency for equilibrium mixture equations of state (2019)
  18. Guermond, Jean-Luc; Popov, Bojan; Saavedra, Laura; Yang, Yong: Arbitrary Lagrangian-Eulerian finite element method preserving convex invariants of hyperbolic systems (2019)
  19. Ibanez, D. A.; Love, E.; Voth, T. E.; Overfelt, J. R.; Roberts, N. V.; Hansen, G. A.: Tetrahedral mesh adaptation for Lagrangian shock hydrodynamics (2019)
  20. Lipnikov, Konstantin; Morgan, Nathaniel: A high-order conservative remap for discontinuous Galerkin schemes on curvilinear polygonal meshes (2019)

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