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Focusing Phenomenon in Numerical Solution of Two-Dimensional Navier–Stokes Equation

  • Tapan K. SenguptaEmail author
  • V. K. Suman
Chapter
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 592)

Abstract

The phenomenon of focusing is associated with abrupt blow-up of numerical solution, after the simulation has gone on for a very long computing time, to exclude the possibility of numerical instability of the method used. In recent times, this phenomenon has been explained for three time-level methods to be due to numerical absolute instability at discrete location, using 1D convection equation as the model equation. Here, we show the focusing of numerical solution of the Navier–Stokes equation, when the two time-level fourth order Runge-Kutta method is used with the sixth order accurate combined compact difference scheme for the closed flow inside a square lid-driven cavity. We relate the phenomenon of focusing here with the numerical anti-diffusion noted for parameter combination for the linearized version of the Navier–Stokes equation, namely the two-dimensional convection-diffusion equation. In the process, we identify critical numerical Peclet number for a chosen CFL number. We show virtually, one to one correspondence between the anti-diffusion of convection-diffusion equation with abrupt blow up the numerical solution of the Navier–Stokes equation.

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Copyright information

© CISM International Centre for Mechanical Sciences 2019

Authors and Affiliations

  1. 1.High Performance Computing Laboratory, Department of Aerospace EngineeringIndian Institute of Technology KanpurKanpurIndia

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