FINITE-DIFFERENCE SCHEMES ON REGULAR TRIANGULAR GRIDS

The phase error and isotropy properties of various finite-difference schemes on grids consisting of regular triangles are compared with similar schemes on square grids. The comparisons are based on a Fourier analysis of semidiscrete solutions to the two-dimensional linear convection equation. The finite-difference schemes presented on the triangular grid include a second-order method, a compact fourth-order method, and a modified compact method designed to extend the accurate wave number range of the numerical approximation. All of the schemes considered are centered and hence nondissipative. In each case, the finite-difference scheme on the triangular grid reduces the anisotropy of the phase error in comparison with a similar scheme on the square grid. © 1993 Academic Press, Inc.