# [lammps-users] granular simulations: choosing the timestep

Dear all,

I have been doing MD simulations for some time, but I am new to granular
simulations, and I am looking for help regarding the choice of the timestep in
simulations of granular gases.

I have the feeling that it should be significantly lower than the collision
time between the particules; I found somewhere that the latter can be
estimated as:

tau ~ (m^2/(R E^2 V))^(1/5) ~ R/V^(1/5)*(rho/E)^(2/5)

where m is the effective mass, R the effective radius, E the effective Young's
modulus, and V the relative velocity of the particules. The collision time can
therefore be computed given the grains size, material and the temperature of
the gas (T = <V>^2/3).

With my student, we chose to work in SI units, in order to compare our results
more directly with the experiments. But using realistic values for a gas of
silica particles with 1mm diameter and maximum velocity around 1m/s, we get an
extremely small timestep.

The trick would be to reduce significantly the elastic constants Kn and Kt of
the particules but then we would lose the one to one correspondance with
experiments...

Do you have some experience/advice on this subject? I would be interested to
know how the timestep is usually chosen. In fact I'm also looking for advices
on the choice of the pair/style gran parameters. Are they usually chosen so as
to reproduce some experimental systems?

Thank you,
Best regards,

Laurent Joly

Most people do granular simulations in reduced (LJ) units,
which can always be mapped to SI (or any other units) after
the fact. You certainly need a timestep smaller than the
collision time (time the 2 particles are in contact), b/c
you have to integrate thru the collision time accurately to
get a valid collision and push-off. If your
particles are very hard, then that time is very short, and you
are stuck with a small timestep. In the LJ world people play
various games with softening the potentials to expand the
timestep. I would read some of the papers on the LAMMPS
pub site with G Grest as an author, for granular systems. They
will discuss a canoncial granular LJ model, and you can convert
the values to SI to see if you agree with them. You might also
ask yourself, what will change in my model if the particles are
somewhat softer? Perhaps nothing significant.

Steve

Hi Laurent,
Typically the time step selected in the MD simulations are taken as 1/50th of the binary collision time. So dt= t_col/50, and t_col is indeed the function of normal stiffness (k_n), effective mass(m) and damping coefficient(\gamma_n). Selecting a typical value for normal stiffness is little tricky, if you increase the k_n (normal stiffness) your required time step would be very less but you will close to realistic values of particle stiffness. Generally we use a value of kn of O(10^5), which one believes captures the general behavior of intermediate to high kn systems. In practice we would like to restrict the initial overlap between the particles less than 5%, to make sure that particles are not too softened.

I would recommend you to read the following two papers which gives the basic idea about doing DEM simulations of granular particles,

Silbert et al., “Granular flow down an inclined plane: Bagnold scaling and rheology”, Physical Review E, Volume 64, 051302.
Campbell C.S., “Granular shear flows at the elastic limit”, J. Fluid Mech., vol. 465, pp. 261-291.

Reagrds,
Vidya