Review of adaptive-grid techniques for solution of partial differential equations

This report summarizes the results of a literature search for adaptive numerical methods of solving partial differential equations; the methods discussed involve the adaptive movement of nodes, so as to obtain a low level of solution truncation error while minimizing the number of nodes used in the calculation. Such methods are applicable to the solution of blast-wave or other nonstationary flow problems that contain moving regions of rapid change in the flow variables, surrounded by regions of relatively smooth variation. Shock waves, contact surfaces, phase-change interfaces, boundary layers and other structures, can be modelled in detail by these methods. It will be shown that significant economies of execution can be attained if nodes are moved so that they remain concentrated in regions of rapid variation of the flow variables.