Reflections on the evolution of implicit Navier-Stokes algorithms

This article gives a historical perspective on the evolution of implicit algorithms for the Navier-Stokes equations that utilize time or Newton linearizations and various forms of approximate factorization including alternating-direction, lower/upper, and symmetric relaxation schemes. A theme of the paper is how progress in implicit Navier-Stokes algorithms has been influenced and enabled by the introduction of characteristic-based upwind approximations, unstructured-grid discretizations, parallelization, and by advances in computer performance and architecture. Historical examples of runtime, problem size, and estimated cost are given for actual and hypothetical Navier-Stokes flow cases from the past 40 years. (C) 2010 Elsevier Ltd. All rights reserved.