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.