Fig 1.
Rectangular 2D lattice illustrating the D2Q9 scheme for the LBM.
Fig 2.
Results of an LBM calculation for a lid-driven cavity, with the geometry (a), streamlines (b), and normalized velocity components u/u0 (c) and v/u0 (d).
Table 1.
Calculation times and calculation speeds for various LBM calculations.
Fig 3.
Sound waves are generated by imposing the fluid density at a lattice node, according to a harmonically oscillating function around an equilibrium value.
Fig 4.
Results of an LBM calculation for a sound wave, showing the sound field at time 1600 (a) and the sound level as a function of source-receiver distance (b).
Fig 5.
As Fig 4, for a point source and receivers at height y = 50.
Fig 6.
LBM results and analytic solutions from Fig 5B, expressed as the excess sound level ΔL (sound level minus free-field level) as a function of distance.
Fig 7.
Results of an LBM calculation for a source and receivers at y = 250 and a porous medium below y = 200, showing the sound field at time 1600 (a) and the sound level as a function of distance (b).
Fig 8.
Stationary vertical velocity field (a) and density field (b) in a 100x100 LBM system with a porous medium between y = 25 and y = 75 and an upward inflow condition at y = 0, used for estimating the flow resistivity.
Fig 9.
LBM results and analytic solutions for porous and non-porous ground, expressed as the excess sound level ΔL as a function of distance.
Fig 10.
Results of an LBM calculation for a non-porous ground surface with a noise barrier at x = 1100 (black line), showing the sound field at time 1600 (a) and the sound level as a function of distance (b).
Fig 11.
LBM result from Fig 10 and analytic solutions, expressed as the excess sound level ΔL as a function of distance.
Fig 12.
Free-field sound level as a function of source-receiver distance, for five values of the kinematic viscosity.
Fig 13.
As Fig 11, but now for kinematic viscosity ν = 0.01.
Fig 14.
As Fig 13, but now for a system with halved lattice spacing.
Fig 15.
As Fig 6, but now for now for a system with ν = 0.01 and halved lattice spacing.
Fig 16.
Schematic illustration of a Poiseuille flow profile.
Fig 17.
LBM results for a system with a sound source in a Poiseuille flow profile.
Figure (a) shows the horizontal velocity component. Figure (b) shows the density field. Figure (c) shows the excess sound level ΔL at receivers near the lower wall (at the same height as the source, i.e. two lattice spacings above the lower wall).
Fig 18.
Schematic illustration of upward and downward refraction of sound waves.
Red lines represent curved sound rays.