Divergence-free velocity fields in nonperiodic geometries
Journal of Computational Physics
Spectral element—Fourier methods for incompressible turbulent flows
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
Efficient Spectral-Galerkin Methods III: Polar and Cylindrical Geometries
SIAM Journal on Scientific Computing
B-spline method and zonal grids for simulations of complex turbulent flows
Journal of Computational Physics
Spectral element methods for axisymmetric Stokes problems
Journal of Computational Physics
An efficient spectral-projection method for the Navier--Stokes equations in cylindrical geometries
Journal of Computational Physics
Velocity-Correction Projection Methods for Incompressible Flows
SIAM Journal on Numerical Analysis
The choice of spectral element basis functions in domains with an axis of symmetry
Journal of Computational and Applied Mathematics
Euro-Par 2008 Workshops - Parallel Processing
Pattern Matching and I/O Replay for POSIX I/O in Parallel Programs
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
A primitive-variable formulation for simulation of time-dependent incompressible flows in cylindrical coordinates is developed. Spectral elements are used to discretise the meridional semi-plane, coupled with Fourier expansions in azimuth. Unlike previous formulations where special distributions of nodal points have been used in the radial direction, the current work adopts standard Gauss-Lobatto-Legendre nodal-based expansions in both the radial and axial directions. Using a Galerkin projection of the symmetrised cylindrical Navier-Stokes equations, all geometric singularities are removed as a consequence of either the Fourier-mode dependence of axial boundary conditions or the shape of the weight function applied in the Galerkin projection. This observation implies that in a numerical implementation, geometrically singular terms can be naively treated by explicitly zeroing their contributions on the axis in integral expressions without recourse to special treatments such as l'Hopital's rule. Exponential convergence of the method both in the meridional semi-plane and in azimuth is demonstrated through application to a three-dimensional analytical solution of the Navier-Stokes equations in which flow crosses the axis.