مجلة الاربعين المحكمة
In this paper ,we use one of mathematical crowd models to represent the movement of crowds arriving for the Arbaeen pilgrimage Specifically, we aim to understand the dynamics of crowds on the road between the two holy mosques. Firstly, we introduce the proposed Mathematical crowd motion. In this model, we define a spontaneous speed corresponding to the speed each individual would like to reach in the absence of others. The actual speed is then calculated as a projection of the spontaneous speed onto a set of feasible speeds (i.e., speeds that do not violate the non-interference constraint). Secondly, the numerical computations are conducted using finite difference method and projection techniques. We also perform numerical simulations using an (Open AI, 2025).The obtained results can assist in designing emergency exits, reducing congestion, and improving crowd distribution.