# Lid-driven Cavity benchmark in 3D. Classical paper to compare

I'm looking for a benchmark for the lid-driven cavity problem in 3D to compare the results of my code.

In 2D I used:

U. K. N. G. Ghia, K. N. Ghia and C. T. Shin (1982) High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of computational physics.

Do you know a benchmark work for the cavity driven in 3D? Which is the classic paper to compare 3D codes?

## 2 Answers

I consider this to be the "classic" 3D-Lid-Driven Cavity (LDC) incompressible flow benchmark paper:

Guj, G. & Stella, F. A vorticity-velocity method for the numerical of 3D incompressible flows. J. Comput. Phys. 298, 286–298 (1993).

Additionally, I developed a 200 line 3-D LDC incompressible flow solver in fortran:

https://github.com/charliekawczynski/short_LDC_fortran

The results from this code look good, but I have not compared them with literature yet.

On a side note perhaps, I think it's funny how the Ghia paper is still used as the benchmark 35 years later on. It had indeed produced great results for its time, but this being a computational problem means their accuracy was limited by the available computer power of the time and today they seem under-resolved. Actually I don't think Ghia et al. even tried to get more accuracy, since they report running times of minutes, aiming to showcase the efficiency of the multigrid method more than to produce benchmarks I think. Little did they know people would still be comparing against their numbers decades later! But any budget laptop now is more than a million times faster than the mainframe Ghia used and multigrid or not, one can easily do a lot better with even a basic implementation. And since we are using this as a benchmark then why not use the more accurate available solutions now? For up to Re 1000 one can look at this 1998 Botella and Peyret paper and for Re up to 30000 here.

• Botella, O., and R. Peyret. "Benchmark spectral results on the lid-driven cavity flow." Computers & Fluids 27.4 (1998): 421-433.