Comparison of method of lines and finite difference solutions of 2‐D Navier–Stokes equations for transient laminar pipe flow

Abstract

AbstractPerformances of method of lines (MOL) and finite difference method (FDM) were tested from the viewpoints of solution accuracy and central processing unit (CPU) time by applying them to the solution of time‐dependent 2‐D Navier–Stokes equations for transient laminar flow without/with sudden expansion and comparing their results with steady‐state numerical predictions and measurements previously reported in the literature. Predictions of both methods were obtained on the same computer by using the same order of spatial discretization and the same uniform grid distribution. Axial velocity and pressure distribution in pipe flow and steady‐state reattachment lengths in sudden expansion flow on uniform grid distribution predicted by both methods were found to be in excellent agreement. Transient solutions of both methods for pipe flow problem show favourable comparison and are in accordance with expected trends. However, non‐physical oscillations were produced by both methods in the transient solution of sudden expansion pipe flow. MOL was demonstrated to yield non‐oscillatory solutions for recirculating flows when intelligent higher‐order discretization scheme is utilized for convective terms. MOL was found to be superior to FDM with respect to CPU and set‐up times and its flexibility for incorporation of other conservation equations. Copyright © 2001 John Wiley & Sons, Ltd.