Journal of Scientific Computing

, Volume 21, Issue 2, pp 225–250 | Cite as

A Comparative Study of Time Advancement Methods for Solving Navier–Stokes Equations

  • T. K. Sengupta
  • A. Dipankar

Abstract

A qualitative and quantitative study is made for choosing time advancement strategies for solving time dependent equations accurately. A single step, low order Euler time integration method is compared with Adams–Bashforth, a second order accurate time integration strategy for the solution of one dimensional wave equation. With the help of the exact solution, it is shown that the presence of the computational mode in Adams–Bashforth scheme leads to erroneous results, if the solution contains high frequency components. This is tested for the solution of incompressible Navier–Stokes equation for uniform flow past a rapidly rotating circular cylinder. This flow suffers intermittent temporal instabilities implying presence of high frequencies. Such instabilities have been noted earlier in experiments and high accuracy computations for similar flow parameters. This test problem shows that second order Adams– Bashforth time integration is not suitable for DNS.

DNS time integration methods dispersion relation preservation Navier–Stokes equation flow instabilities 

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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • T. K. Sengupta
  • A. Dipankar
    • 1
  1. 1.Department of Aerospace EngineeringI.I.TKanpurIndia

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