A comparison of adaptive-grid redistribution and embedding for steady transonic flows

In recent years, numerical analysts have increasingly turned to adaptive grid techniques to efficiently obtain highly-accurate solutions to partial-differential equations. This paper presents a comparison of two distinct grid adaptation approaches, grid-point redistribution and grid embedding, applied to two-dimensional, steady, inviscid, shocked flows. Grid redistribution is accomplished through a control function approach applied to the elliptic grid-generator while the embedding approach consists of a fixed global grid and an automatically-chosen number of irregularly-shaped, embedded regions. For both techniques, the Euler flow equations are integrated to steady-state using Ni’s Lax-Wendroff-type integrator to predict the flow fields about a variety of isolated airfoil configurations. The application of a common integration scheme as well as a common adaptive control function leads to a direct comparison of the effectiveness of the two adaptation approaches for the types of problems tested.