Computer-Extended Series in Fluid Mechanics

Abstract

A still unconventional use of the computer in fluid mechanics is to extend a regular perturbation series to high order. Using even a desk computer, one can calculate dozens of terms for a nonlinear partial differential equation, and hundreds of terms for a linear one. However, the result is ordinarily so limited that it needs improvement. A second step is therefore to analyze the coefficients to unveil the analytic structure of the solution in the complex plane of the perturbation quantity. On that basis, one can undertake the third step of applying a variety of devices for extending and improving the convergence. This three-step process will be discussed and illustrated by examples from various branches of fluid mechanics.