Solution of the Navier‐Stokes equations by the spectral‐difference method

Abstract

AbstractThe Jacobi polynomial collocation method is extended to two and three dimensions by superimposing the individual one‐dimensional expansions. Two innovative ideas are introduced in this article. The first is the cornerless/edgeless computational grid, and the second is the modified compressibility method, which is an iterative pressure solver. To evaluate the new method's applicability in solving the Navier‐Stokes equation, the lid‐driven cavity flow problem was solved. Two configurations were considered, the square cavity and the rectangular cavity with an aspect ratio of 2. A comparison of the center‐line velocity profiles from two‐ and three‐dimensional simulations at a Reynolds number of 1000 is provided for each of the configurations. The center‐line velocity comparisons showed good quantitative agreement with previous studies. © 1994 John Wiley & Sons, Inc.