464 The lattice Boltzmann method for fluid dynamics
derivative) of the parabola is given by∇P/(νρ). Check also that the velocity v
which is added at each step is related to the pressure byρ v=∇P/c.Inthe
simulation, we usually take the lattice constant xand the time step tequal to 1.
Check that the velocity profile of your simulation matches the result for
ν=( 2 τ− 1 )/6.
14.2 [C] Extend the simulation of the parabolic flow by putting an object in the flow. This
can be a fixed block. Check your results by inspecting the flow in the channels on
both sides of the block to see whether the total flow is the same through the
rectangular pipe.
14.3 [C] Write a program for droplet formation in a binary system along the lines
indicated in Section 14.4.
14.4 [C] In this problem we check Laplace’s law. In order to do this, you need to identify
the droplets and find the pressure drop across their boundaries. To this end you step
over all lattice sites and check whether there is a large predominance of one colour.
If this is the case, you use either the back-track or the Hoshen–Kopelman algorithm
which are both described in Section 15.5.1, in order to identify all sites.
Furthermore, you store the largest pressure value in the current droplet.
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