A 3D pseudospectral method for cylindrical coordinates. Application to the simulations of rotating cavity flows

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

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

The present work proposes a collocation spectral method for solving the three-dimensional Navier-Stokes equations using cylindrical coordinates. The whole diameter -R < r < R is discretized with an even number of radial Gauss-Lobatto collocation points and an angular shift is introduced in the Fourier transform that avoid pole and parity conditions usually required. The method keeps the spectral convergence that reduces the number of grid points with respect to lower-order numerical methods. The grid-points distribution densifies the mesh only near the boundaries that makes the algorithm well-suited to simulate rotating cavity flows where thin layers develop along the walls. Comparisons with reliable experimental and numerical results of the literature show good quantitative agreements for flows driven by rotating discs in tall cylinders and thin inter-disc cavities. Associated to a spectral vanishing viscosity [E. Séverac, E. Serre, A spectral vanishing viscosity for the LES of turbulent flows within rotating cavities, J. Comp. Phys. 226 (2007) 1234-1255], the method provides very promising LES results of turbulent cavity flows.

Mots clés: Rotor-stator flow; Cylindrical coordinates; Pseudospectral method; Collocation method

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

Noele Peres, Sébastien Poncet, Eric Serre. A 3D pseudospectral method for cylindrical coordinates. Application to the simulations of rotating cavity flows. Journal of Computational Physics, 2012, 231, pp.6290-6305. ⟨10.1016/j.jcp.2012.04.033⟩. ⟨hal-00822026⟩