Chemistry Reference
In-Depth Information
This collision test is evaluated for every possible colliding pair within the sys-
tem by looping over all molecules and calculating the next collision time for each.
From these times, a table of collision times is created containing predictions for
when each sphere will have its next collision. The calculation of this table is the
last step in the initialization stage.
The table can then be used and updated in the equilibrium and production
stages to advance the simulation and evaluate the next collision.
Collisions are modelled as binary interactions, occurring instantaneously,
where the molecules exchange linear momentum.
1.4.4.1 Time steps
The first task in the time step loop is to look at the table of predicted collision
times and find which collision will occur next. The first collision to happen is the
only reliable prediction as the collisions afterwards may occur in a different order.
The simulation is then progressed by advancing to the time of this collision and
moving all spheres using
r
(
t
+
t
)
=
r
(
t
)
+
v
(
t
)
t
.
(1.61)
The new position for each sphere,
r
(
t
t
), is calculated from the old position,
r
(
t
), by adding the distance travelled at constant velocity,
+
t
. When
all spheres have been moved, the two that are colliding will be in contact and the
momentum exchange can take place. As the masses of the spheres are the same,
the mass terms can be cancelled out of the momentum equation completely, leav-
ing just an exchange of velocity. The velocities of the two spheres are projected
along the line of their centres, as in the two-dimensional example in Figure 1.17.
At the collision, the component of velocity along the line connecting the two
v
(
t
), during
Figure 1.17
Hard sphere collision evaluation. Momentum is transformed from physical
coordinates along the line between the centres of the molecules, along which they exchange
momentum.
Search WWH ::
Custom Search