Pole condition for singular problems: the pseudospectral approximation
Journal of Computational Physics
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
A pseudospectral approach for polar and spherical geometries
SIAM Journal on Scientific Computing
A spectral method for polar coordinates
Journal of Computational Physics
A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates
Journal of Computational Physics
Journal of Computational Physics
Numerical treatment of polar coordinate singularities
Journal of Computational Physics
Highly energy-conservative finite difference method for the cylindrical coordinate system
Journal of Computational Physics
Journal of Computational Physics
A family of low dispersive and low dissipative explicit schemes for flow and noise computations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
In this paper, the errors generated by the computation of derivatives in the azimuthal direction @q when flow equations are solved in cylindrical coordinates using finite differences are investigated. They might be large for coarse discretizations even using high-order schemes, which led us to design explicit finite differences specially for 8, 16, 32 and 64 points per circle. These schemes are shown to improve accuracy with respect to standard finite differences, and to provide solutions for a two-dimensional propagation problem similar to those obtained using Fourier spectral methods in the direction @q. A method is then presented to alleviate the time-step limitation resulting from explicit time integration near cylindrical origin, when finite differences are used. It consists in calculating azimuthal derivatives at coarser resolutions than permitted by the grid, in the same way as usually done using spectral methods. In practice, a series of doublings of the effective discretization in @q is implemented. Thus simulations can for instance be performed on a grid containing n"@q=256 points with a time step 32 times larger, with an accuracy comparable to that achieved in corresponding simulations involving Fourier spectral methods in the direction @q.