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ÖgeCrowding behavior of oil an introductory modeling studies(Graduate School, 20210522)We introduce an introductory modeling studies for representation of crowding behavior of surface oil slick using a random walk process for Particles dispersion, while the advection process is approximated with the help of a Runge–Kutta method. Voronoi diagram updated at each time step to help in using Voronoi diagram to calculate the area associated with each particle and the corresponding oil thickness and calculate an additional velocity that depends on the maximum gradient of the oil thickness. Tracking particles in the current implementation and due to the simple 2D geometry, a scheme inspired by finite differences was used here. The whole domain is discretized using a structured grid and each cell (in this case a small square) is associated with one or more history variables that describe the current state of the system. As long as the introduced particles represent oil droplets with some thickness then it is reasonable to prevent accumulating infinite number of these particles in one cell. Hence, a limiting variable is introduce to control the maximum amount of particles allowed to be simultaneously in the same cell. When this limit is reached then no more particles are allowed to enter the cell then we calculate the direction of maximum gradient and that is the largest difference between the thickness around the cells and the particles are moving to neighbour cells. Voronoi diagram updated at each time step to help in using Voronoi diagram to calculate the area associated with each particle and the corresponding oil thickness and calculate an additional velocity that depends on the maximum gradient of the oil thickness (repulsive velocity). What we doing is we are advection the particles we are dispersion the particle and then when the particles push into the wall they start to crowding over each other and when it gets too crowded and can't stay top of each other, so too crowded particles start to separate from each other and that what we called the repulsive effect. When the particles reach the steady state we drop down the advection current in the geometry to zero and checked the repulsive effect separately. We get a smooth field by using Scatterinterpolate and shading interp function in the Matal.