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Simulating the collision behaviour of cloud drops in a turbulent environment is numerically expensive. Because of the typical sizes of cloud drops, their motion is predominantly influenced by the smallest turbulent scales in the flow. We can exploit this property by using an Arnold--Beltrami--Childress (ABC) flow instead of a full direct numerical simulation (DNS) to simulate the turbulent effect on cloud drop collisions. This allows simulation of drop motion using much less computational resources than needed by DNS and therefore, allows for simulations with many more drops and larger model domains or more complex cloud physics. This is useful in cases where a specific process needs to be studied and the complexity and details of a realistic turbulent flow are of secondary interest. It is shown that the simulations using ABC flow can faithfully reproduce collision statistics from much more comprehensive DNS calculations when using a similar Taylor microscale and root mean square velocity in the ABC and DNS flows. The results from the ABC flow are robust to changes in these two parameters within a reasonable range, even though adjustments to the parameters can be used to further tune the results.