NUMERICAL TREATMENT OF CYLINDRICAL COORDINATE SINGULARITIES

Noele Peres (1) , Sébastien Poncet (1) , Eric Serre (1)

1 M2P2 - Modélisation et Simulation Numérique (en mécanique des fluides)

The present work proposes direct numerical simulations of some rotating disk flows using a pseudo-spectral method with collocation Chebyshev polynomials in the radial and axial directions and Fourier approximation in the periodic azimuthal direction. When using cylindrical coordinates to calculate the Navier-Stokes equations the singularity that appears on the axis (r = 0), because of the terms 1/r and 1/r2 is only apparent. To avoid evaluating differential equation coefficients which are infinite the spectral grid must exclude the origin. The interesting issue is how does one impose boundary conditions at the origin? With spectral methods, there are various ways to avoid this difficulty without prescribing any pole conditions. In this work, we have developed a method which consists in discretizing the whole diameter −R ≤ r ≤ R with an even number of radial Gauss-Lobatto nodes. In the azimuthal direction, the overlap in the discretization is avoided by introducing a shift equal to Pi /2K (K the number of mesh points in that direction) for Theta>Pi in the Fourier transform. Spectral convergence of the method is illustrated on an analytical solution. The ability of our numerical method to investigate complex unsteady flows is illustrated for three rotating flows where other reliable experimental and numerical results are available.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Noele Peres, Sébastien Poncet, Eric Serre. NUMERICAL TREATMENT OF CYLINDRICAL COORDINATE SINGULARITIES. V European Conference on Computational Fluid Dynamics (ECCOMAS CFD 2010), Jun 2010, Lisbonne, Portugal. ⟨hal-00679115⟩