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

Validation: 3D Coupled Lattice Boltzmann and Finite Difference, Laminar flow, Heat Transfer

Description

Laminar flow and convective heat transfer in a heated square cavity. Flow is heated on the left side of the cavity more than the right, creating buoyancy induced circulation and run to steady state.

The top and bottom walls are adiabatic (zero gradient), all walls are no-slip. The modelled domain is a thin slice, periodic in the spanwise direction.

Figure 1: Flow domain

Simulation Inputs

Input	Value
Material Properties	Density = incompressible, ideal gas. Kinematic viscosity = 5.05 × 10⁻⁴ m²/s. Thermal diffusivity = 7.11 × 10⁻⁴ m²/s. Prandtl number = 0.71.
Geometry	L = H = 1.0 m, W = 0.03125 m.
Boundary Conditions	T_h − T_c = 1 K, T₀ = 273.15 K. Buoyancy body force from Boussinesq approximation (g = 9.81 m/s²). Rayleigh number = 10⁵.

Assumptions and Notes

Flow is incompressible, steady and laminar. Fluid density is based on the incompressible gas assumption, and applied using the Boussinesq approximation.

Results

Vertical velocity at mid-height, Ra = 10⁵

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 2: Vertical velocity at mid-height, Ra = 10⁵

Mid-height profiles, Ra = 10⁵: Wan et al. (DSC) vs FlowDeck

x/L	v, Wan et al.	v, FlowDeck	θ, Wan et al.	θ, FlowDeck
0.0	0.0000	0.0000	1.00000	1.00000
0.1	63.2531	60.3999	0.59351	0.59666
0.2	16.2278	15.1597	0.46987	0.47260
0.3	−0.6499	1.0517	0.48355	0.48079
0.4	−1.8263	−0.2623	0.49772	0.49421
0.5	−0.0038	0.0006	0.49968	0.50001
0.6	1.8189	0.2627	0.50165	0.50578
0.7	0.6394	−1.0495	0.51583	0.51919
0.8	−16.2428	−15.1563	0.52952	0.52742
0.9	−63.2326	−60.4060	0.40597	0.40328
1.0	0.0000	0.0000	0.00000	0.00000

Temperature at mid-height, Ra = 10⁵

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: Temperature at mid-height, Ra = 10⁵

Values are in the table under Figure 2.

Velocity magnitude field in the buoyancy driven cavity — Figure 4: Velocity magnitude field, Ra = 10⁵

Reference Data

The reference is the high-accuracy benchmark of Wan et al. [1] for 10³ ≤ Ra ≤ 10⁸. Velocities are scaled by κ/L and temperature normalised as

θ = \frac{T - T_{c}}{T_{h} - T_{c}}

References

D. C. Wan, B. S. V. Patnaik and G. W. Wei, “A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution,” Numerical Heat Transfer, Part B: Fundamentals 40(3), 199–228, 2001. doi:10.1080/104077901752379620

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.