During flood discharge atomization

collision between the water nappes and the water body in the downstream scour pool causes numerous water droplets to splash out in random directions. This creates an initial value problem for the movement of splashing water droplets. This paper develops a concept of number theory graded water droplets

which adopts the number theory method to grade water droplets

based on the idea that this method maintains good uniformity even with a small number of selected points. Using the concept

we can simplify the high dimensional phase space to one-dimensional

and develop a mathematical model for simulation of random splashing water droplets using number theory classification. Comparison of the numerical calculations with the high-accuracy solution reveals that the error of our model is lower for a given number of droplets. As the number of droplets increases

the error decreases at a faster rate and approaches the high-precision solution more rapidly. Thus

by simulating random splashing water droplets using number theory classification

this new model not only achieves higher calculation accuracy with a smaller number of droplets

but simplifies the expression of the high dimensional initial value phase space to one-dimensional.