Question: please write matlab code for advection-diffusion An oil spill is detected near a protected island area in the Pacific Ocean. NOAA (National Occanic and Atmospheric

An oil spill is detected near a protected island area in the Pacific Ocean. NOAA (National Occanic and Atmospheric Agency) has requested you to simulate the movement and distrubution of the pollution (advection-diffusion) towards the protected island area. The location and geometry of the problem is given in the following figure: (0,10) (10,10) (3.5,6.5) (5,6.5) (6.5,6.5) (3.5,5). Protected Island . (6.5,5) (3.5,3.5) (5,3.5) (6.5,3.5) L 0.5 1 (0,0) (0,10) Additional infromation: The entire simulation domain is 10 by 10 kilometers The protcted island can be simplified by a square 1.8 by 1.8 km domain (green square) Oil has a lighter unit weight than water (therefore will not sink under the water) Coefficient of diffusion (in both x and y direction) D=D=0.008 km /h Concentration of the pollution = 5000 (kg/km) & measurement stations are placed around the island to measure any impurity in the water. The coordinates of the measurement statios can be found in the below figure: (3.5,6,5) (5,6.5) (6.5,6.5) (3.5,5) Protected . (6.5,5) (3.5,3.5) (5,3.5) (6.5,3.5) NOAA is asking you to perform simulation for the following 3 scenarios: Case I) Vx=2 km/h, Vy-2.5 km/h Case II) V=2 km/h, Vy=2 km/h Case III) V=1.5 km/h, Vy=1.5 km/h Deliverables: The FDM toolkit built in MATLAB (m files) The simulation animation performed for the total time of 20 hours The concentration of oil spill at the 8 measurement stations over the entire time of simulation Which velocity field case (I, II or III) result in the worst case scenario for the protected island. Stability Condition: Vdt Vydt D dt Dydt + + dx dy (dx)2 + (dy)2
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