ReALE

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. 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)
  2. Florez, Sebastian; Alvarado, Karen; Muñoz, Daniel Pino; Bernacki, Marc: A novel highly efficient Lagrangian model for massively multidomain simulation applied to microstructural evolutions (2020)
  3. 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)
  4. Kenamond, Mack; Shashkov, Mikhail: The distribution-based remapping of the nodal mass and momentum between arbitrary meshes for staggered arbitrary Lagrangian-Eulerian hydrodynamics (2020)
  5. Schnücke, Gero; Krais, Nico; Bolemann, Thomas; Gassner, Gregor J.: Entropy stable discontinuous Galerkin schemes on moving meshes for hyperbolic conservation laws (2020)
  6. Zhang, Chao; Menshov, Igor: Eulerian model for simulating multi-fluid flows with an arbitrary number of immiscible compressible components (2020)
  7. Guermond, Jean-Luc; Popov, Bojan; Saavedra, Laura; Yang, Yong: Arbitrary Lagrangian-Eulerian finite element method preserving convex invariants of hyperbolic systems (2019)
  8. Qing, Fang; Yu, Xijun; Jia, Zupeng: A robust MoF method applicable to severely deformed polygonal mesh (2019)
  9. Yang, Haihua; Zhang, Ping: A hybrid subcell-remapping algorithm for staggered multi-material arbitrary Lagrangian-Eulerian methods (2019)
  10. Zhang, Chao; Menshov, Igor: Using the composite Riemann problem solution for capturing interfaces in compressible two-phase flows (2019)
  11. Anderson, Robert W.; Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.; Tomov, Vladimir Z.: High-order multi-material ALE hydrodynamics (2018)
  12. Burton, D. E.; Morgan, N. R.; Charest, M. R. J.; Kenamond, M. A.; Fung, J.: Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme (2018)
  13. Gaburro, Elena; Dumbser, Michael; Castro, Manuel J.: Reprint of: “Direct arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming unstructured meshes” (2018)
  14. Morgan, Nathaniel R.; Liu, Xiaodong; Burton, Donald E.: Reducing spurious mesh motion in Lagrangian finite volume and discontinuous Galerkin hydrodynamic methods (2018)
  15. Pei, Chaoxu; Sussman, Mark; Hussaini, M. Yousuff: A space-time discontinuous Galerkin spectral element method for the Stefan problem (2018)
  16. Perumal, Logah: A brief review on polygonal/polyhedral finite element methods (2018)
  17. Semplice, Matteo; Loubère, Raphaël: Adaptive-mesh-refinement for hyperbolic systems of conservation laws based on a posteriori stabilized high order polynomial reconstructions (2018)
  18. Barral, N.; Olivier, G.; Alauzet, F.: Time-accurate anisotropic mesh adaptation for three-dimensional time-dependent problems with body-fitted moving geometries (2017)
  19. Basting, Steffen; Quaini, Annalisa; Čanić, Sunčica; Glowinski, Roland: Extended ALE method for fluid-structure interaction problems with large structural displacements (2017)
  20. Boscheri, Walter: High order direct arbitrary-Lagrangian-Eulerian (ALE) finite volume schemes for hyperbolic systems on unstructured meshes (2017)

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