Performance of r-Adaptation Using Truncation Error-Based Equidistribution

This paper investigates the computational cost of performing r-adaptation by equidistributing the truncation error. This adaptation approach is applied to several two-dimensional (2D) problems using the Euler and laminar Navier–Stokes equations. The costs of performing the adaptation are compared to uniform refinement, and it is shown that adaptation can be far cheaper than uniform refinement. This paper also presents a new method of refining the equidistributed meshes. This new approach allows the adaptation to be performed on much coarser meshes and provides a method of refining these coarse, adapted meshes to meet a discretization-error target for the problem. We show that this approach can be at least 16–24 times cheaper than uniform refinement for the problems investigated here. This approach also is at least ten times faster than performing r-adaptation on a fine enough mesh to obtain the target discretization-error level.