An immiscible, binary fluid lattice Boltzmann model is described
and its associated
equations of motion are given. It is seen that the lattice Boltzmann scheme is
totally isotropic and that it does not suffer from the problems of
noisy results
and a lack of
Galilean invariance which plagued its predecessor: the
lattice gas model.
The incorporation of a body force into the
lattice Boltzmann technique is considered. A method which introduces the
body force directly into the governing equation is proposed
and is seen to have the desired effect without destroying the
Galilean invariance of the original model and without introducing any
dependency on the grid orientation.
The immiscible, binary fluid model, with the body force incorporated,
is applied to simulate interfacial waves between the two
fluids. The model parameters allow the interface thickness,
the fluid viscosity, the gravitational strength
and the relative density of the two fluids
to be varied. The wavelength
of the wave can also be set during the wave initialisation. Standing
waves are simulated for a wide range of the variable parameters and
progressive waves for a subset of the parameters.
The results are seen to compare well
with linear wave theory. When compared
with available experimental results the behaviour is seen to be
similar.