A comparison of time integration methods in an unsteady low-Reynolds-number flow

This paper describes three different time integration methods for unsteady incompressible Navier–Stokes equations. Explicit Euler and fractional-step Adams–Bashford methods are compared with an implicit three-level method based on a steady-state SIMPLE method. The implicit solver employs a dual time stepping and an iteration within the time step.

The spatial discretization is based on a co-located finite-volume technique. The influence of the convergence limits and the time-step size on the accuracy of the predictions are studied. The efficiency of the different solvers is compared in a vortex-shedding flow over a cylinder in the Reynolds number range of 100–1600.

A high-Reynolds-number flow over a biconvex airfoil profile is also computed. The computations are performed in two dimensions. At the low-Reynolds-number range the explicit methods appear to be faster by a factor from 5 to 10. In the high-Reynolds-number case, the explicit Adams–Bashford method and the implicit method appear to be approximately equally fast while yielding similar results.

Copyright © 2002 John Wiley & Sons, Ltd.