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Results

The completed parameter study contains 72 configured cases:

3 meshes × 3 Reynolds numbers × 2 schemes × 2 pressure solvers × 2 implementations

The numerical summary is available in assets/data/study_summary.csv.

Overview

Result Value
Executed cases 72
Cases within the selected Ghia error limits 44
Cases that met the strict outer stopping criteria before maxIter 0
Passes at N = 32 8 / 24
Passes at N = 64 12 / 24
Passes at N = 128 24 / 24

Every case reached its configured outer-iteration limit. Some still matched the Ghia centerline data reasonably well, but profile error and numerical convergence are not the same thing. The summary reports them separately.

Mesh and Reynolds-number effects

The mesh trend is clear:

  • all 24 cases at Re = 100 met the selected limits
  • at Re = 400, 12 of 24 cases met them
  • at Re = 1000, 8 of 24 cases met them
  • all 24 cases on the N = 128 mesh met them

This is not a formal grid-independence study, but it shows the expected loss of accuracy when a coarse mesh is used at a higher Reynolds number.

Ghia error by mesh

Upwind and central differencing

Central differencing met the selected limits in 24 of 36 cases, compared with 20 of 36 for upwind.

On better-resolved cases, central differencing generally followed the benchmark more closely. Upwind was more forgiving on coarse meshes, but its added numerical diffusion weakened the velocity gradients.

Pressure-solver performance

The pressure solve was the main computational cost.

Pressure solver Mean pressure iterations per outer iteration Mean total case runtime*
RBGS about 1333 about 1841 s
RBSOR about 265 about 458 s

*Runtime values are specific to the machine and settings used to generate the included summary. They compare configured executions and are not time-to-convergence measurements.

RBSOR had a much larger effect on total runtime than vectorizing the momentum predictor.

Pressure solver comparison

Loop and vectorized implementations

Equivalent loop and vectorized cases produced matching numerical results. Their average total runtimes were close:

  • loop: about 1157 s
  • vectorized: about 1142 s

The small difference shows that optimizing the momentum predictor alone has limited effect while the pressure solve remains the bottleneck.

Implementation runtime comparison

Completed scope and possible follow-up research

The repository records the completed MATLAB implementation and 72-case configuration. Possible follow-up research includes:

  1. revisiting stopping criteria and relaxation settings
  2. improving collocated pressure-velocity treatment with Rhie-Chow interpolation
  3. replacing or accelerating the pressure solver
  4. running a dedicated grid-independence study
  5. comparing vortex locations and strengths in addition to centerline velocities

These are extensions to the completed baseline, not missing claims from the recorded study.