Name: Poiseuille Flow validation
Creator: FlowDeck
License: https://creativecommons.org/licenses/by/4.0/

Validation: 2D Lattice Boltzmann, Laminar flow

Description

Laminar, fully developed channel flow in a 2D domain. Flow is driven by a uniform body force and run to a steady state. Half of the domain plane is modelled.

One boundary is a no-slip wall, the opposite boundary is a symmetry plane at the channel centreline, and the inlet and outlet and two spanwise faces are periodic.

Figure 1: Flow domain: half channel

Simulation Inputs

Input	Value
Material Properties	Density = 1.0 kg/m³, Viscosity = 0.144 m²/s
Geometry	W/2 = H = 0.5m
Boundary Conditions	Body force: $F_{y} = 8 ν u_{0} / (W^{2})$ where $u_{0}$ is centre-line velocity (1.0 m/s).

Assumptions and Notes

Flow is incompressible and steady.

Results

The simulated velocity profile at mid-length matches the analytical parabola to round-off precision.

Streamwise velocity field in the half channel — Figure 2: Streamwise velocity field

Velocity profile at mid-length vs analytical solution

Hover or tap the chart to read the values at any point. Click a legend item to show or hide it. Half of the channel is modelled, so FlowDeck values run from the wall to the centreline.

Figure 3: Velocity profile at mid-length vs analytical solution

Velocity at mid-length: analytical vs FlowDeck

x/W	Analytical u/u₀	FlowDeck u/u₀	Error
0.00	0.00	–	–
0.05	0.19	0.19	0.00
0.15	0.51	0.51	0.00
0.25	0.75	0.75	0.00
0.35	0.91	0.91	0.00
0.45	0.99	0.99	0.00
0.55	0.99	–	0.00
0.65	0.91	–	0.00
0.75	0.75	–	0.00
0.85	0.51	–	0.00
0.95	0.19	–	0.00
1.00	0.00	–	–

Reference Data

Analytical solution is the steady momentum balance between the body force and viscous shear, which gives the parabolic profile [1]:

ν \frac{d^{2} u_{y}}{d x^{2}} = - F_{y}

u_{y} (x) = \frac{F_{y}}{2 ν} (W x - x^{2}), (u_{y} (0) = 0, u_{y} (W) = 0)

References

T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva and E. M. Viggen, The Lattice Boltzmann Method: Principles and Practice, Springer, Cham, 2017. doi:10.1007/978-3-319-44649-3

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.