Applied Computational Fluid Dynamics Techniques: An Introduction Based on Finite Element Methods, 2nd Edition

14 ADAPTIVE MESH REFINEMENT

The development of self-adaptive mesh refinement techniques in computational fluid dynamics (CFD), computational structural dynamics (CSD), computational electromagnetics (CEM) and other fields of computational mechanics is motivated by a number of factors.

(a) With mesh adaptation, the numerical solution to a specific problem, given the basic accuracy of the solver and the desired accuracy, should be achieved with the fewest degrees of freedom. This, in most cases, translates into the least amount of work for a given accuracy. Work in this context should be understood as meaning not only CPU, but also memory and man-hour requirements.

(b) For some classes of problems, the savings in CPU and memory requirements exceed a factor of 100 (see Baum and Löhner (1989)). This is equivalent to two generations of supercomputing. For these problems, adaptive mesh refinement has acted as an enabling technology, allowing the simulation of previously intractable problems.

(c) Mesh adaptation avoids time delays incurred by trial and error in choosing a grid that is suitable for the problem at hand. Although this may seem unimportant for repetitive steady-state calculations, it is of the utmost importance for transient problems with travelling discontinuities (shocks, plastic fronts, etc.). In this way, adaptation adds a new dimension of user-friendliness to computational mechanics.

Given these very strong motivating reasons, the last two decades have seen a tremendous ...