A spectral/B-spline method for the Navier-Stokes equations in unbounded domains

  • Authors:

  • L. Dufresne;G. Dumas

  • Affiliations:

  • Département de Génie Mécanique, Université Laval, Que., Canada G1K 7P4 and Unite TERM, Département de Mécanique, Université Catholique de Louvain, B-1348 Louvain ...;Département de Génie Mécanique, Université Laval, Que., Canada G1K 7P4

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2003

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Abstract

The numerical method presented in this paper aims at solving the incompressible Navier-Stokes equations in unbounded domains. The problem is formulated in cylindrical coordinates and the method is based on a Galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint. More specifically, the divergence-free basis vector functions are constructed with Fourier expansions in the θ and z directions while mapped B-splines are used in the semi-infinite radial direction. Special care has been taken to account for the particular analytical behaviors at both end points r = 0 and r → ∞. A modal reduction algorithm has also been implemented in the azimuthal direction, allowing for a relaxation of the CFL constraint on the timestep size and a possibly significant reduction of the number of DOF. The time marching is carried out using a mixed quasi-third order scheme. Besides the advantages of a divergence-free formulation and a quasi-spectral convergence, the local character of the B-splines allows for a great flexibility in node positioning while keeping narrow bandwidth matrices. Numerical tests show that the present method compares advantageously with other similar methodologies using purely global expansions.