Discretization of Navier-Stokes equations on moving unstructured meshes

Authors

Keywords:

unstructured mesh, moving mesh, finite-volume method, computational gas dynamics

Abstract

Some approaches to discretization of Navier-Stokes equations on moving unstructured meshes, methods of mesh evolution on every time step, and finite difference schemes satisfying the geometric conservation law are discussed. Numerical simulation of inviscid compressible gas flow around a linear profile cascade performing small harmonic vibrations is performed. The results obtained are compared with available computational and experimental data. Keywords: unstructured mesh, moving mesh, finite-volume method, computational gas dynamics

Author Biography

K.N. Volkov

References

  1. Haber R., Shephard M.S., Abel J.F., Gallagher R.H., Greenberg D.P. A general two-dimensional graphical finite-element preprocessor utilizing discrete transfinite mappings // International Journal for Numerical Methods in Engineering. 1981. 17, N 7. 1015-1044.
  2. Gadala M.S., Movahhedy M.R., Wang J. On the mesh motion for ALE modeling of metal forming processes // Finite Elements Analysis Design. 2002. 38, N 5. 435-459.
  3. Batina J.T. Unsteady euler airfoil solutions using unstructured dynamic meshes // AIAA Journal. 1990. 28, N 8. 1381-1388.
  4. Venkatakrishnan V., Mavriplis D.J. Implicit method for the computation of unsteady flows on unstructured grids // Journal of Computational Physics. 1996. 127, N 2. 380-397.
  5. Johnson A.A., Tezduyar T.E. Simulation of multiple spheres falling in a liquid-filled tube // Computer Methods in Applied Mechanics and Engineering. 1996. 134, N 3/4. 351-373.
  6. Farhat C., Degand C., Koobus B., Lesoinne M. Torsional spring for two-dimensional dynamic unstructured fluid meshes // Computer Methods in Applied Mechanics and Engineering. 1998. 163, N 1/4. 231-245.
  7. Blom F.J. Considerations on the spring analogy // International Journal for Numerical Methods in Engineering. 2000. 32, N 6. 647-668.
  8. Nielsen E.J., Anderson W.K. Recent improvements in aerodynamic design optimization on unstructured meshes // AIAA Journal. 40, N 6. 1155-1163.
  9. Souli M., Zolesio J.P. Arbitrary Lagrangian -Eulerian and free surface methods in fluid mechanics // Computer Methods in Applied Mechanics and Engineering. 2001. 191, N 3/5. 451-466.
  10. Degand C., Farhat C. A three-dimensional torsional spring analogy method for unstructured dynamic meshes // Computers and Structures. 2002. 80, N 3/4. 305-316.
  11. Murayama M., Nakahashi K., Matsushima K. Unstructured dynamic mesh for large movement and deformation // AIAA Paper N 2002-0122. 2002.
  12. Bottasso C.L., Detomi D., Serra R. The ball-vertex method: a new simple analogy method for unstructured dynamic meshes // Computer Methods in Applied Mechanics and Engineering. 2005. 194, N 39/41. 4244-4264.
  13. Zeng D., Ethier C.R. A semi-torsional spring analogy model for updating unstructured meshes in 3D moving domains // Finite Elements in Analysis and Design. 2005. 41, N 11/12. 1118-1139.
  14. Markou G.A., Mouroutis Z.S., Charmpis D.C., Papadrakakis M. The ortho-semi-torsional (OST) spring analogy method for 3D mesh moving boundary problems // Computer Methods in Applied Mechanics and Engineering. 2007. 196, N 4/6. 747-765.
  15. Yan S., Ma Q.W. Numerical simulation of fully nonlinear interaction between steep waves and 2D floating bodies using the QALE-FEM method // Journal of Computational Physics. 2007. 221, N 1. 666-692.
  16. Thomas P.D., Lombard C.K. Geometric conservation law and its application to flow computations on moving grids // AIAA Journal. 1979. 17, N 10. 1030-1037.
  17. Lesoinne M., Farhat C. Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations // Computer Methods in Applied Mechanics and Engineering. 1996. 134, N 1/2. 71-90.
  18. Koobus B., Farhat C. Second-order time-accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes // Computer Methods in Applied Mechanics and Engineering. 1999. 170, N 1/2. 103-129.
  19. Gordnier R.E., Melville R.B. Transonic flutter simulations using an implicit aeroelastic solver // AIAA Journal of Aircraft. 2000. 37, N 5. 872-879.
  20. Guillard H., Farhat C. On the significance of the geometric conservation law for flow computations on moving meshes // Computer Methods in Applied Mechanics and Engineering. 2000. 190, N 11/12. 1467-1482.
  21. Farhat C., Geuzaine P., Crandmont C. The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids // Journal of Computational Physics. 2001. 174, N 2. 669-694.
  22. Jothiprasad G., Mavriplis D.J., Caughey D.A. Higher-order time integration schemes for the unsteady Navier -Stokes equations on unstructured meshes // Journal of Computational Physics. 2003. 191, N 2. 542-566.
  23. Zhang L.P., Wang Z.J. A block LU-SGS implicit dual time-stepping algorithm for hybrid dynamic meshes // Computers and Fluids. 2004. 33, N 7. 891-916.
  24. Yang Z. Unstructured dynamic meshes with higher-order time integration schemes for the unsteady Navier -Stokes equations // AIAA Paper N 2005-1222. 2005.
  25. Mavriplis D.J., Yang Z. Construction of the discrete geometric conservation law for high-order time-accurate simulations on dynamic meshes // Journal of Computational Physics. 2006. 213, N 2. 557-573.
  26. Волков К.Н. Применение метода контрольного объема для решения задач механики жидкости и газа на неструктурированных сетках // Вычислительные методы и программирование. 2005. 6, № 1. 47-64.
  27. Fransson T.H., Verdon J.M. Standard configurations for unsteady flow through vibrating axial-flow turbomachine-cascades // Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines and Propellers. New York: Springer-Verlag, 1993. 859-889.
  28. Lawrence C., Spyropoulos E., Reddy T.S. R. Unsteady cascade aerodynamic response using a multiphysics simulation code // NASA Report N TM 2000-209635. 2000.
  29. Verdon J.M., Caspar J.R. A linearized unsteady aerodynamic analysis for transonic cascades // Journal of Fluid Mechanics. 1984. 149. 403-429.

Published

16-09-2008

How to Cite

Волков К. Discretization of Navier-Stokes Equations on Moving Unstructured Meshes // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2008. 9. 256-273

Issue

Section

Section 1. Numerical methods and applications

Most read articles by the same author(s)

1 2 3 4 > >>