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We Helped With This Differential Equations Homework: Have A Similar One?
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Short Assignment Requirements
Write a matlab code to solve the Lnear advection euqation. Question #1 only.
Finally, we'll be writing a CFD code! We are solving the linear advection equation: Ju əx using a scheme which is first order in space and time: which gives: 0, du axxo,to Ju at xo,to u (xoto + At) = = = Ju Ət = u (xo, to) - u (xo - Ax, to) Ax u (xo, to + At) - u (xo, to) At 600 -C- 0,0625 u (xo, to) - - cAt Ax For all cases, c = 1/2. Our computational domain for this problem is: 1 0≤x≤ 600 Ax = 1 2 3 ui n+l ni - 1 (1) n Ui-I DX Ui (u (xo, to) - u (xo - Ax, to)) (2) st (3)
The initial condition is: ↑ u (x,0) = 1 This equation requires a boundary condition at x = 0, which is: +=0 1. (60/100): For time steps of At u (0, t) = 0.25 + = This value should be used at the x = 0 grid point. All other points should be computed using Eqn (2). At the outflow, no boundary condition is needed; just use the code to compute the flow. Again, you'll be specifying the value of u at the first grid point (x=0) and computing the other 600. Hint from the Professor: Please note that this is a marching method, and computational memory is not infinite. A properly written code does not have to store u for all space and time (601 space points x 14400 time levels), but only at two (at most) time levels (601 space points x 2 time levels) - but one time level is easily possible. Another hint from the Professor: You'll want to debug your code using the smallest time step... Grading: 0.25 cos ( +0.25 cost +0.25 cos (Tot (4) (5) 0.0625,0.125, 0.25, 0.3, 0.4, 0.5, 0.6, 0.75, 0.8, 1.0, 1.2, 1.25, 1.5, 1.8, 2.0, 3.0, 4.0 compute the flow solution at t = 900. Plot the solutions as a function tn=to + Dt of x. ⇒ Dt * No, it = 900 harmonic 2 2. (20/100): Describe the differences (if any) in the solutions. Illustrate your description with graphs of the solutions. Compare the results as necessary to illustrate what's happening in the solutions as the time step is changed. wave