Fluid Physics at Meso Scales - Fluid Properties at Nano/Meso Scale: A Numerical Treatment - page 57

Primary simulation cell

Primary cell surrounded by
copies/images

Figure 2.5 Periodic boundary conditions.

As a molecule passes over the boundary and out of the primary cell and into
an adjoining image, at the same time an identical molecule with exactly the same
properties passes in from the image on the opposite side into the primary cell. In
the case of the soft sphere model, cross boundary interactions also need to be taken
into account by finding the nearest image of an interacting particle. This is best
illustrated by the one dimensional example in Figure 2.6, where it is shown that
as the separation between two molecules becomes greater than a

/

2, the particle
i is nearest to the image of the second particle, j . At the boundaries of the main

Image 1 Primary Cell Image 2

a

i
(image1)

j
(image1)

i
(image2)

i
(image2)

j

i

Particle i's influence

Figure 2.6 Soft sphere cross boundary interaction.