Stokes eigenmodes in cubic domain: primitive variable and Lattice Boltzmann formulations

Applied Numerical Mathematics

Volumn 58, Issue 7, 2008, Pages 935-945

  Leriche, E ^a   Lallemand, P ^b   Labrosse, G ^c  

^a Institut des Sciences de l'Energie   (Switzerland)

^b CNRS   (France)

^c UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Chebyshev spectral method; Lattice Boltzmann method; Stokes eigenmodes

Indexed keywords

BOLTZMANN EQUATION; DIFFUSION; NUMERICAL METHODS; PROBLEM SOLVING;

CHEBYSHEV SPECTRAL METHOD; LATTICE BOLTZMANN METHOD; STOKES EIGENMODES;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 43849090462     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2007.04.012     Document Type: Article

References (20)

1. Batoul A., Khallouf H., and Labrosse G. Une méthode de résolution directe (pseudo-spectrale) du problème de Stokes 2D/3D instationnaire. Application à la cavité entrainée carrée. C. R. Acad. Sci. Paris, Sér. I 319 (1994) 1455-1461
2. Benzi R., Succi S., and Vergassola M. The lattice Boltzmann equation: theory and applications. Phys. Rep. 222 (1992) 145-197
3. Broadwell J.E. Shock structure in a simple discrete velocity gas. Phys. Fluids 7 (1964) 1243
4. Chen S., and Doolen G.D. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluids Mech. 30 (1998) 329-364
5. Constantin P., and Foias C. Navier-Stokes Equations. Chicago Lectures in Mathematics (1988), University of Chicago Press, Chicago
6. Deville M.O., Fischer P.F., and Mund E.H. High-Order Method for Incompressible Fluid Flow (2002), Cambridge University Press, Cambridge
7. d'Humières D. Generalized lattice-Boltzmann equations. In: Shizgal B.D., and Weaver D.P. (Eds). Rarefied Gas Dynamics. Progress in Astronautics and Aeronautics vol. 159 (1992), AIAA, Washington, DC
8. d'Humières D., Bouzidi M., and Lallemand P. Thirteen-velocity three-dimensional lattice Boltzmann model. Phys. Rev. E 63 (2001) 066702
9. Frisch U., d'Humières D., Hasslacher B., Lallemand P., Pomeau Y., and Rivet J.P. Lattice gas hydrodynamics in two and three dimensions. Complex Systems 1 (1987) 649-707
10. Ginzburg I., and d'Humières D. Multireflection boundary conditions for lattice Boltzmann models. Phys. Rev. E 68 (2003) 066614
11. Gottlieb D., and Orszag S.A. Numerical Analysis of Spectral Methods: Theory and Applications (1977), SIAM-CBMS, Philadelphia
12. Hirasaki G.J., and Hellums J.D. Boundary conditions on the vector and scalar potentials in viscous three-dimensional hydrodynamics. Quart. Appl. Math. XXVIII 2 (1970) 293-296
13. Junk M., and Klar A. Discretizations for the incompressible Navier-Stokes equations based on the lattice Boltzmann method. SIAM J. Sci. Comput. 22 1 (2000) 1-19
14. Lallemand P., and Luo L.S. Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance and stability. Phys. Rev. E 61 (2000) 6546-6562
15. Lehoucq R.B., Sorensen D.C., and Yang C. ARPACK Users' Guide (1998), SIAM, Philadelphia
16. Leriche E., and Labrosse G. High-order direct Stokes solvers with or without temporal splitting: Numerical investigations of their comparative properties. SIAM J. Sci. Comput. 22 4 (2000) 1386-1410
17. Leriche E., and Labrosse G. Stokes eigenmodes in square domain and the stream function - vorticity correlation. J. Comput. Phys. 200 2 (2004) 489-511
18. Leriche E., and Labrosse G. Fundamental Stokes eigenmodes in the square: which expansion is more accurate, Chebyshev or Reid-Harris? Numer. Algorithms 38 1-2 (2005) 111-131
19. Leriche E., Perchat E., Labrosse G., and Deville M.O. Numerical evaluation of the accuracy and stability properties of high-order direct Stokes solvers with or without temporal splitting. J. Sci. Comput. 26 1 (2006) 25-43
20. Tinkham M. Group Theory and Quantum Mechanics (1964), McGraw-Hill, New York