Adaptation

Abstract

This chapter focuses on the use of adaptation in solving the Euler equations. Adaptation is the process by which some aspect of the solution algorithm changes in response to an evolving solution. These changes can be in the governing equations [11], in the computational grid, or in both the equations and the grid [29]. In this thesis, adaptation refers to changes in the computational grid as the solution proceeds. In a problem, certain regions of a computational domain will have “interesting” features (shocks, boundary layers, recirculation zones, etc.), while other regions will have smooth and relatively uninteresting flow. The interesting regions are often regions with high gradients and hence larger numerical errors. The idea behind grid adaptation is to increase the number of points in the regions of high error (or gradient) to try and increase overall solution quality at reasonable cost. Several ways of adapting grids are described below. The grid redistribution method attempts to get to an optimal grid for a given number of points. The grid regeneration and grid enrichment methods attempt to reduce the computational cost for a desired level of error.