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. Abreu, Eduardo; François, Jean; Lambert, Wanderson; Pérez, John: A semi-discrete Lagrangian-Eulerian scheme for hyperbolic-transport models (2022)
  2. Asuri Mukundan, Anirudh; Ménard, Thibaut; Brändle de Motta, Jorge César; Berlemont, Alain: A hybrid moment of fluid-level set framework for simulating primary atomization (2022)
  3. Chartrand, Chris; Perot, J. Blair: A method for generating moving, orthogonal, area preserving polygonal meshes (2022)
  4. Chiodi, Robert; Desjardins, Olivier: General, robust, and efficient polyhedron intersection in the interface reconstruction library (2022)
  5. Peluchon, S.; Gallice, G.; Mieussens, L.: Development of numerical methods to simulate the melting of a thermal protection system (2022)
  6. Abgrall, Rémi; Le Mélédo, Élise; Öffner, Philipp: General polytopal (H(\mathrmdiv))-conformal finite elements and their discretisation spaces (2021)
  7. Cheng, Lidong; Deng, Xi; Xie, Bin; Jiang, Yi; Xiao, Feng: Low-dissipation BVD schemes for single and multi-phase compressible flows on unstructured grids (2021)
  8. Chiocchetti, Simone; Peshkov, Ilya; Gavrilyuk, Sergey; Dumbser, Michael: High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension (2021)
  9. De Vuyst, Florian; Fochesato, Christophe; Mahy, Vincent; Motte, Renaud; Peybernes, Mathieu: A geometrically accurate low-diffusive conservative interface capturing method suitable for multimaterial flows (2021)
  10. Kenamond, Mack; Kuzmin, Dmitri; Shashkov, Mikhail: A positivity-preserving and conservative intersection-distribution-based remapping algorithm for staggered ALE hydrodynamics on arbitrary meshes (2021)
  11. Kenamond, Mack; Kuzmin, Dmitri; Shashkov, Mikhail: Intersection-distribution-based remapping between arbitrary meshes for staggered multi-material arbitrary Lagrangian-Eulerian hydrodynamics (2021)
  12. Pezzano, Stefano; Duvigneau, Régis: A NURBS-based discontinuous Galerkin method for conservation laws with high-order moving meshes (2021)
  13. Qing, Fang; Yu, Xijun; Jia, Zupeng; Li, Zhenzhen: A cell-centered Lagrangian discontinuous Galerkin method using WENO and HWENO limiter for compressible Euler equations in two dimensions (2021)
  14. Romeo, F. L.; Dumbser, M.; Tavelli, M.: A novel staggered semi-implicit space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations (2021)
  15. Wu, Wenbin; Zhang, A-Man; Liu, Moubin: A cell-centered indirect arbitrary-Lagrangian-Eulerian discontinuous Galerkin scheme on moving unstructured triangular meshes with topological adaptability (2021)
  16. 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)
  17. Balsara, Dinshaw S.; Garain, Sudip; Florinski, Vladimir; Boscheri, Walter: An efficient class of WENO schemes with adaptive order for unstructured meshes (2020)
  18. Cheng, Jian; Zhang, Fan; Liu, Tiegang: A discontinuous Galerkin method for the simulation of compressible gas-gas and gas-water two-medium flows (2020)
  19. Dobrev, Veselin; Knupp, Patrick; Kolev, Tzanio; Mittal, Ketan; Rieben, Robert; Tomov, Vladimir: Simulation-driven optimization of high-order meshes in ALE hydrodynamics (2020)
  20. 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)

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