Transformations of matrices into banded form
Journal of Computational Physics
Divergence-free velocity fields in nonperiodic geometries
Journal of Computational Physics
Chebyshev pseudospectral method of viscous flows with corner singularities
Journal of Scientific Computing
A spectral method for polar coordinates
Journal of Computational Physics
Journal of Computational Physics
An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries
Journal of Computational Physics
Accurate Navier-Stokes investigation of transitional and turbulent flows in a circular pipe
Journal of Computational Physics
An efficient spectral-projection method for the Navier--Stokes equations in cylindrical geometries
Journal of Computational Physics
Poloidal-toroidal decomposition in a finite cylinder
Journal of Computational Physics
Poloidal-toroidal decomposition in a finite cylinder
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
The Navier-Stokes equations in a finite cylinder are written in terms of poloidal and toroidal potentials in order to impose incompressibility. Regularity of the solutions is ensured in several ways: First, the potentials are represented using a spectral basis which is analytic at the cylindrical axis. Second, the non-physical discontinuous boundary conditions at the cylindrical corners are smoothed using a polynomial approximation to a steep exponential profile. Third, the nonlinear term is evaluated in such a way as to eliminate singularities. The resulting pseudo-spectral code is tested using exact polynomial solutions and the spectral convergence of the coefficients is demonstrated. Our solutions are shown to agree with exact polynomial solutions and with previous calculations of axisymmetric vortex breakdown and of onset of non-axisymmetric helical spirals. Parallelization by azimuthal wavenumber is shown to be highly effective.