Spatial adaptation of unstructured meshes for unsteady aerodynamic flow computations

Abstract

Spatial adaptation procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaptation procedures were developed and implemented within a two-dimensional unstructured-grid upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in high gradient regions of the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational cost. The paper describes a new approach to detect high gradient regions of the flow that uses the substantial derivative of density. Additionally, the paper gives a detailed description of the enrichment and coarsening procedures and further describes a new weighted averaging procedure and the interpolation of flow variables that improves the overall accuracy of the flow solver. Presented are comparisons with alternative results and experimental data to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady transonic results, obtained using spatial adaptation for the NAG A 0012 airfoil, are shown to be of high spatial accuracy, primarily in that the shock waves are very sharply captured. The results were obtained with large computational savings when compared to results for a globally enriched mesh with cells subdivided as many times as the finest cells of the adapted grid.