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A subcell based interface reconstruction method to deal with filaments

A subcell based interface reconstruction method to deal with filaments. Christophe Fochesato 1 , Raphaël Loubère 2 , Renaud Motte 1 , Jean Ovadia 3 1 CEA, DAM, DIF, F-91297 Arpajon, France 2 Institut de Mathématiques de Toulouse, CNRS, Université de Toulouse

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A subcell based interface reconstruction method to deal with filaments

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  1. A subcell based interface reconstruction method to deal with filaments Christophe Fochesato1, Raphaël Loubère2,Renaud Motte1, Jean Ovadia3 1CEA, DAM, DIF, F-91297 Arpajon, France 2Institut de Mathématiques de Toulouse, CNRS, Université de Toulouse 3Retired fellow from CEA, CESTA, F-33114 Le Barp, France MULTIMAT 2011, Arcachon

  2. I Introduction Context / Problem / Proposed solution / Example II Presentation of the method Detection / Sub-zones / Volume distribution / Reconstruction III Test cases Some static filaments / Mesh dependency III Work in progress Defects to be corrected First advections Conclusions / Perspectives Outline MULTIMAT 2011, Arcachon

  3. I Introduction MULTIMAT 2011, Arcachon

  4. bi-fluid hydrodynamical flows with interfaces • VoF interface reconstruction • maximum possible resolution is not always sufficient • structure size < mesh cell size I - Context MULTIMAT 2011, Arcachon

  5. usual VoF methods use only one interface per mixed cell, typically a straight line (PLIC) • numerical surface tension • generation of flotsam reduces robustness • Youngs’ normal can be irrelevant: ~0 because of almost symmetrical volume fractions on the stencil • reconstruction is inaccurate although there is enough information to do better with the same 9-cells stencil I - Problem MULTIMAT 2011, Arcachon

  6. work in two steps: improve static reconstruction / advection • the idea is to compute subgradients from a local stencil associated with each corner (2x2 cells for instance) in order to reconstruct up to 4 interfaces, one per subzone, with normals given by these subgradients • method does not contain more physics • another geometrical choice • with less numerical surface tension • avoiding to use irrelevant normal information • localized algorithm in the code: no change in the numerical scheme I – Proposed solution : a subgradients method MULTIMAT 2011, Arcachon

  7. our VoF implementation with Youngs’ normal I - Example VoF / subgradients with PLIC per subzone MULTIMAT 2011, Arcachon

  8. II Presentation of the method MULTIMAT 2011, Arcachon

  9. detection of marked cells • subgradients computation • determination of subzones for reconstruction: 1, 2, 3 or 4 • distribution of fluid per subzone • Youngs/PLIC reconstruction: one straight line per subzone II – Method summary MULTIMAT 2011, Arcachon

  10. 0 0.3 0.1 0 0 0.5 0.4 0 0.1 • computation of a volume fraction gradient per cell • the cell is marked • if normal is potentially not relevant: or • if the fluid potentially passes through the cell II – Detection of marked cells f7 f8 f9 f4 f6 f5 f1 f2 f3 MULTIMAT 2011, Arcachon

  11. only for marked cells • compute a gradient associated with each corner on a 2x2 stencil • confirmation that cell must be considered • if gradient is less relevant than subgradients • or • if the fluid really passes through the cell • or • if a filament end is found c k II – Computation of subgradients 0 0 0 0 0.5 0.6 0 0 0 0.4 0 0.8 0 0.5 0.6 0 0 0 MULTIMAT 2011, Arcachon

  12. keep only relevant subgradients • with relevant subgradients, we associate subzones • 4 relevant subgradients • 3 relevant subgradients • 2 relevant subgradients • 1 relevant subgradient II – Determination of subzones MULTIMAT 2011, Arcachon

  13. use of a prescribed formula from the 9-cells stencil • Correction if more volume of fluid than volume of the subzone • uniform scattering on other non full subzones 0.1 . 0 0 0 0 0.5 II – Distribution of the volume of fluid 0 0.1 0.5 0.1 0.5 0.5 0 0.5 0.1 0.5 0 0 MULTIMAT 2011, Arcachon

  14. PLIC per subzone • Youngs’ algorithm II – Reconstruction of interfaces MULTIMAT 2011, Arcachon

  15. III Test Cases MULTIMAT 2011, Arcachon

  16. cartesian grid • gradients computation with Youngs’ Finite Difference formula • subgradients computation with Finite Difference formula • Lagrange + remap scheme with direction splitted remapping • interface reconstruction on 1D-stretched cells for each direction • exact intersection of transfered volume of the cell with reconstructed interface gives transfered volume for the fluid III – Implementation used for the tests MULTIMAT 2011, Arcachon

  17. filaments to be reconstructed • - Lagrangian objects remapped on the grid III – Static filaments MULTIMAT 2011, Arcachon

  18. with VoF / PLIC III – Static filaments MULTIMAT 2011, Arcachon

  19. with subgradients III – Static filaments MULTIMAT 2011, Arcachon

  20. III – Static filaments MULTIMAT 2011, Arcachon

  21. III – Static filaments MULTIMAT 2011, Arcachon

  22. III – Static filaments MULTIMAT 2011, Arcachon

  23. III – Static filaments MULTIMAT 2011, Arcachon

  24. III – Static filaments MULTIMAT 2011, Arcachon

  25. III – Static filaments MULTIMAT 2011, Arcachon

  26. III – Static filaments MULTIMAT 2011, Arcachon

  27. III – Mesh dependency • shifted by Δx / 4 • smallerfilament width MULTIMAT 2011, Arcachon

  28. III – Mesh dependency • shifted by Δx/ 4 • rotated by 10o MULTIMAT 2011, Arcachon

  29. IV Work in progress MULTIMAT 2011, Arcachon

  30. relative position in the cell is not known • the method tends to locate the fluid to the center of the cell • the idea is to extrapolate the location of the intersection point of the subdivision from the fluid presence in the 9-cells stencil • connexity is not guaranteed • correction algorithm after reconstruction is possible IV – Defects to be corrected MULTIMAT 2011, Arcachon

  31. III – First advection cases MULTIMAT 2011, Arcachon

  32. III – First advection cases MULTIMAT 2011, Arcachon

  33. Conclusions, perspectives MULTIMAT 2011, Arcachon

  34. summary • a subgradient method to compute VoF/PLIC interfaces in subzones • at given mesh, better representation of thin structures of fluid • not a subgrid physical model: method as geometrical as original VoF with the same volume fraction field information • tends to locate the fluid to the center of the cell • connexity not guaranteed • for advection, necessity of new information : • … natural extension to 3D • … natural extension to unstructured mesh • … no obvious extension to more than 2 fluids Conclusions, perspectives in progress perspectives MULTIMAT 2011, Arcachon

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