Efficient Moving Mesh Technique Using Generalized Swapping

Summary

Three-dimensional real-life simulations are generally unsteady and involve moving geometries. Industries are currently still very far from performing such simulations on a daily basis, mainly due to the robustness of the moving mesh algorithm and their extensive computational cost. The proposed approach is a way to improve these two issues. This paper brings two new ideas. First, it demonstrates numerically that moving three-dimensional complex geometries with large displacements is feasible using only vertex displacements and mesh-connectivity changes. This is new and presents several advantages over usual techniques for which the number of vertices varies in time. Second, most of the CPU time spent to move the mesh is due to the resolution of the mesh deformation algorithm to propagate the body displacement inside the volume. Thanks to the use of advanced meshing operators to optimize the mesh, we can reduce drastically the number of such resolutions thus impacting favorably the CPU time. The efficiency of this new methodology is illustrated on numerous 3D problems involving large displacements.

Keywords

Moving mesh mesh deformation algorithm dynamic mesh topology change swapping local reconnection elasticity equation large displacement 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alauzet, F., Belme, A., Dervieux, A.: Anisotropic Goal-Oriented Mesh Adaptation for Time Dependent Problems. In: Quadros, W.R. (ed.) Proceedings of the 20th International Meshing Roundtable, vol. 90, pp. 99–121. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. 2.
    Alauzet, F., Mehrenberger, M.: P1-conservative solution interpolation on unstructured triangular meshes. Int. J. Numer. Meth. Engng 84(13), 1552–1588 (2010)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Alauzet, F., Olivier, G.: Extension of metric-based anisotropic mesh adaptation to time-dependent problems involving moving geometries. In: 49th AIAA Aerospace Sciences Meeting, AIAAP 2011-0896, Orlando, FL, USA (January 2011)Google Scholar
  4. 4.
    Baker, T.J., Cavallo, P.: Dynamic adaptation for deforming tetrahedral meshes. AIAA Journal 19, 2699–3253 (1999)Google Scholar
  5. 5.
    Batina, J.: Unsteady Euler airfoil solutions using unstructured dynamic meshes. AIAA Journal 28(8), 1381–1388 (1990)CrossRefGoogle Scholar
  6. 6.
    Baum, J.D., Luo, H., Löhner, R.: A new ALE adaptive unstructured methodology for the simulation of moving bodies. In: 32nd AIAA Aerospace Sciences Meeting, AIAAP 1994-0414, Reno, NV, USA (January 1994)Google Scholar
  7. 7.
    Benek, J.A., Buning, P.G., Steger, J.L.: A 3D chimera grid embedding technique. In: 7th AIAA Computational Fluid Dynamics Conference, AIAA Paper 1985-1523, AIAAP 1985-1523, Cincinnati, OH, USA (July 1985)Google Scholar
  8. 8.
    Compere, G., Remacle, J.-F., Jansson, J., Hoffman, J.: A mesh adaptation framework for dealing with large deforming meshes. Int. J. Numer. Meth. Engng 82(7), 843–867 (2010)MATHGoogle Scholar
  9. 9.
    de Boer, A., van der Schoot, M., Bijl, H.: Mesh deformation based on radial basis function interpolation. Comput. & Struct. 85, 784–795 (2007)CrossRefGoogle Scholar
  10. 10.
    Dobrzynski, C., Frey, P.J.: Anisotropic Delaunay mesh adaptation for unsteady simulations. In: Proceedings of the 17th International Meshing Roundtable, pp. 177–194. Springer (2008)Google Scholar
  11. 11.
    Frey, P.J., George, P.L.: Mesh generation. Application to finite elements, 2nd edn. ISTE Ltd and John Wiley & Sons (2008)Google Scholar
  12. 12.
    George, P.L.: Tet meshing: construction, optimization and adaptation. In: Proceedings of the 8th International Meshing Roundtable, South Lake Tao, CA, USA (1999)Google Scholar
  13. 13.
    George, P.L., Borouchaki, H.: Construction of tetrahedral meshes of degree two. Int. J. Numer. Meth. Engng 90, 1156–1182 (2012)CrossRefMATHGoogle Scholar
  14. 14.
    Hassan, O., Probert, E.J., Morgan, K., Weatherill, N.P.: Unsteady flow simulation using unstructured meshes. Comput. Methods Appl. Mech. Engrg. 189, 1247–1275 (2000)CrossRefMATHGoogle Scholar
  15. 15.
    Löhner, R.: Extensions and improvements of the advancing front grid generation technique. Communications in Numerical Methods in Engineering 12, 683–702 (1996)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Löhner, R., Yang, C.: Improved ALE mesh velocities for moving bodies. Comm. Numer. Meth. Engnr 12(10), 599–608 (1996)CrossRefMATHGoogle Scholar
  17. 17.
    Luke, E., Collins, E., Blades, E.: A fast mesh deformation method using explicit interpolation. J. Comp. Phys. 231, 586–601 (2012)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Marcum, D.L.: Unstructured grid generation using automatic point insertion and local reconnection. Revue Européenne des Éléments Finis 9, 403–423 (2000)Google Scholar
  19. 19.
    Olivier, G., Alauzet, F.: A new changing-topology ALE scheme for moving mesh unsteady simulations. In: 49th AIAA Aerospace Sciences Meeting, AIAA Paper 2011-0474, Orlando, FL, USA (January 2011)Google Scholar
  20. 20.
    Peskin, C.S.: Flow patterns around heart valves: a numerical method. J. Comp. Phys. 10, 252–271 (1972)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Stein, K., Tezduyar, T., Benney, R.: Mesh moving techniques for fluid-structure interactions with large displacements. Jour. Appl. Mech. 70, 58–63 (2003)CrossRefMATHGoogle Scholar
  22. 22.
    Thomas, P.D., Lombard, C.K.: Geometric conservation law and its application to flow computations on moving grids. AIAA Journal 17(10), 1030–1037 (1979)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Yang, Z., Mavriplis, D.J.: Higher-order time integration schemes for aeroelastic applications on unstructured meshes. AIAA Journal 45(1), 138–150 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Domaine de VoluceauINRIA RoquencourtLe ChesnayFrance

Personalised recommendations