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Grid sensitivity and role of error in computing a lid-driven cavity problem.

V K Suman1, Siva Viknesh S1, Mohit K Tekriwal1

  • 1High Performance Computing Laboratory, Indian Institute of Technology Kanpur, Kanpur-208 016 India.

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Summary

This study investigates grid sensitivity in lid-driven cavity (LDC) flow bifurcations using high-accuracy parallel algorithms. Results reveal numerical errors and disturbances are interchangeable, impacting critical Reynolds numbers.

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Area of Science:

  • Fluid dynamics
  • Computational science
  • Numerical analysis

Background:

  • The critical Reynolds number for lid-driven cavity (LDC) flow bifurcations varies across studies due to numerical methods and grid choices.
  • Understanding these variations is crucial for accurate simulation of LDC flow physics.

Purpose of the Study:

  • To perform a grid sensitivity investigation for the bifurcation problem of canonical LDC flow.
  • To present high-accuracy results using very fine grids to resolve discrepancies in critical Reynolds numbers.
  • To analyze the interplay between numerical errors and flow disturbances.

Main Methods:

  • Employed a very-high-accuracy parallel algorithm with uniform grids of (1025×1025) and (2049×2049) points.
  • Utilized the same numerical method as Lestandi et al. for direct comparison.
  • Implemented explicit excitation to study numerical receptivity and flow stability.

Main Results:

  • Demonstrated that numerical errors and ambient disturbances can be interchangeable in LDC flow simulations.
  • Identified a threshold amplitude for explicit excitation below which the flow returns to a quiescent state.
  • Presented near spectral accuracy results, establishing universal benchmarks for Navier-Stokes solutions in LDC.

Conclusions:

  • Grid sensitivity significantly affects bifurcation predictions in LDC flow.
  • Numerical errors must be carefully managed and understood in relation to physical disturbances.
  • The study provides benchmark data for validating numerical schemes for LDC flow simulations.