Abstract
An efficient and accurate numerical scheme is presented for the axisymmetric Navier-Stokes equations in primitive variables in a cylinder. The scheme is based on a new spectral-Galerkin approximation for the space variables and a second-order projection scheme for the time variable. The new spectral-projection scheme is implemented to simulate the unsteady incompressible axisymmetric flow with a singular boundary condition which is approximated to within a desired accuracy by using a smooth boundary condition. A sensible comparison is made with a standard second-order (in time and space) finite difference scheme based on a stream function-vorticity formulation and with available experimental data. The numerical results indicate that both schemes produce very reliable results and that despite the singular boundary condition, the spectral-projection scheme is still more accurate (in terms of a fixed number of unknowns) and more efficient (in terms of CPU time required for resolving the flow at a fixed Reynolds number to within a prescribed accuracy) than the finite difference scheme. More importantly, the spectral-projection scheme can be readily extended to three-dimensional nonaxisymmetric cases.
Original language | English (US) |
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Pages (from-to) | 308-326 |
Number of pages | 19 |
Journal | Journal of Computational Physics |
Volume | 139 |
Issue number | 2 |
DOIs | |
State | Published - Jan 20 1998 |
Externally published | Yes |
ASJC Scopus subject areas
- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics