Application of a multi-level grid method to transonic flow calculations

A multi-level grid method has been studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse (e.g., 8 x 2 mesh cells) to fine (e.g., 128 x 32); the coarser grids are used to diminish the magnitude of the smooth part of the residuals, hopefully with far less total work than would be required with, say, optimal SLOR iterations on the finest grid. The method was applied to the solution of the transonic small-disturbance equation for the velocity potential in the conservation form. Nonlifting transonic flow past a parabolic-arc airfoil is the example studied, with meshes of both constant and variable step size.