Name: Lid Driven Cavity validation
Creator: FlowDeck
License: https://creativecommons.org/licenses/by/4.0/

Validation: 3D Lattice Boltzmann, Laminar flow

Description

Laminar, recirculating flow inside a square cavity. Flow is driven by a constant speed sliding wall and run to steady state. A slice is run in 3D, with the flow only changing in 2 dimensions.

The top lid moves in its own plane, the other three walls are stationary and no-slip. The domain is a thin slab, periodic in the spanwise direction.

Figure 1: Flow domain

Simulation Inputs

Input	Value
Material properties	Density = 1.0 kg/m³. Kinematic viscosity ν = UL/Re = 1.0 × 10⁻² m²/s (Re = 100), 2.5 × 10⁻³ m²/s (Re = 400), 1.0 × 10⁻³ m²/s (Re = 1000).
Geometry	L = H = 1.0 m, W = 0.03125 m.
Boundary Conditions	Lid speed (U) = 1.0 m/s. Reynolds number varies from 100, 400, 1000 by Re = UL/ν.

Assumptions and Notes

Flow is incompressible and steady.

Results

Velocity magnitude field in the lid driven cavity — Figure 2: Velocity magnitude field, Re = 10,000

Horizontal velocity on the vertical centre line, x = 0.5L

Hover or tap the chart to read the values at any point. Click a legend item to show or hide it. FlowDeck values are at cell centres; the lines are completed with the wall boundary values.

Figure 3: Horizontal velocity on the vertical centre line, x = 0.5L

u/U on the vertical centre line: Ghia et al. vs FlowDeck

y/L	Ghia, Re = 100	FlowDeck, Re = 100	Ghia, Re = 400	FlowDeck, Re = 400	Ghia, Re = 1000	FlowDeck, Re = 1000
1.0000	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000
0.9766	0.84123	0.84373	0.75837	0.75970	0.65928	0.66152
0.9688	0.78871	0.79199	0.68439	0.68605	0.57492	0.57617
0.9609	0.73722	0.74056	0.61756	0.61837	0.51117	0.50977
0.9531	0.68717	0.69114	0.55892	0.55945	0.46604	0.46253
0.8516	0.23151	0.23573	0.29093	0.28540	0.33304	0.32404
0.7344	0.00332	0.00336	0.16256	0.15909	0.18719	0.18147
0.6172	−0.13641	−0.13779	0.02135	0.01974	0.05702	0.05436
0.5000	−0.20581	−0.20619	−0.11477	−0.11539	−0.06080	−0.06029
0.4531	−0.21090	−0.21059	−0.17119	−0.17151	−0.10648	−0.10464
0.2813	−0.15662	−0.15474	−0.32726	−0.31997	−0.27805	−0.27247
0.1719	−0.10150	−0.09985	−0.24299	−0.23226	−0.38289	−0.37231
0.1016	−0.06434	−0.06325	−0.14612	−0.13817	−0.29730	−0.28125
0.0703	−0.04775	−0.04578	−0.10338	−0.09730	−0.22220	−0.20742
0.0625	−0.04192	−0.04122	−0.09266	−0.08714	−0.20196	−0.18800
0.0547	−0.03717	−0.03656	−0.08186	−0.07693	−0.18109	−0.16815
0.0000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000

Vertical velocity on the horizontal centre line, y = 0.5L

Hover or tap the chart to read the values at any point. Click a legend item to show or hide it. FlowDeck values are at cell centres; the lines are completed with the wall boundary values.

Figure 4: Vertical velocity on the horizontal centre line, y = 0.5L

v/U on the horizontal centre line: Ghia et al. vs FlowDeck

x/L	Ghia, Re = 100	FlowDeck, Re = 100	Ghia, Re = 400	FlowDeck, Re = 400	Ghia, Re = 1000	FlowDeck, Re = 1000
1.0000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000
0.9688	−0.05906	−0.06132	−0.12146	−0.12052	−0.21388	−0.21394
0.9609	−0.07391	−0.07684	−0.15663	−0.15540	−0.27669	−0.27537
0.9531	−0.08864	−0.09198	−0.19254	−0.19049	−0.33714	−0.33343
0.9453	−0.10313	−0.10685	−0.22847	−0.22552	−0.39188	−0.38594
0.9063	−0.16914	−0.17403	−0.23827*	−0.37563	−0.51550	−0.50587
0.8594	−0.22445	−0.22939	−0.44993	−0.44152	−0.42665	−0.41528
0.8047	−0.24533	−0.24875	−0.38598	−0.37863	−0.31966	−0.30810
0.5000	0.05454	0.05703	0.05188	0.05364	0.02526	0.02606
0.2344	0.17527	0.17662	0.30174	0.29435	0.32235	0.31507
0.2266	0.17507	0.17641	0.30203	0.29442	0.33075	0.32312
0.1563	0.16077	0.16194	0.28124	0.27294	0.37095	0.35991
0.0938	0.12317	0.12405	0.22965	0.22205	0.32627	0.31504
0.0781	0.10890	0.10960	0.20920	0.20184	0.30353	0.29265
0.0703	0.10091	0.10156	0.19713	0.19002	0.29012	0.27946
0.0625	0.09233	0.09293	0.18360	0.17679	0.27485	0.26438
0.0000	0.00000	0.00000	0.00000	0.00000	0.00000	0.00000

* Ghia et al. give v = −0.23827 at x = 0.9063 for Re = 400. This value is widely regarded as a misprint in the original table (it breaks the smooth profile), so it is left out of the chart.

Reference Data

The reference is the multigrid benchmark of Ghia et al. [1] for 100 ≤ Re ≤ 10,000, computed on 129² and 257² grids. Velocities are scaled by the lid speed, with the Reynolds number:

Re = \frac{U L}{ν}

References

U. Ghia, K. N. Ghia and C. T. Shin, “High-Re solutions for incompressible flow using the Navier–Stokes equations and a multigrid method,” Journal of Computational Physics 48(3), 387–411, 1982. doi:10.1016/0021-9991(82)90058-4

Data licence. The model results on this page and in the CSV downloads are published by FlowDeck under the Creative Commons Attribution 4.0 licence (CC BY 4.0). The reference values are from the sources listed under References.