# hw1 - For the first time step use an Euler(1 st order time...

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Numerical Methods for Coastal and Oceanographic Engineering Slinn Spring 2004 Home Work Problem # 1. Due January 27, 2004. Solve the one way wave equation, 0 = + x u C t u , using second and fourth order explicit methods. A. Use second order Leap Frog time difference and central spatial differences on the domain, 0 < x < 10 m, on the time interval, 0 < t < 6 s, with C = 1 m s -1 , with initial conditions u . Let x = 0.1 m (101 grid points). 2 ) 2 ( 5 3 ) 0 , ( = x e x The exact result should look like u . Plot this together with your solution for C 2 ) 8 ( 5 3 ) 6 , ( = x e x fl = 0.1, 0.99, and 1.2. For boundary conditions use u = 0 at x = 0, 10 m at all times.
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Unformatted text preview: For the first time step, use an Euler (1 st order) time step. B. Repeat using ∆ x = 0.01 and 0.5 m, with C fl = 0.99. C. Compare the solutions for the L-F method at t = 6 s and t = 6 - ∆ t s for C fl = 0.99. D. Repeat using 4 th order central spatial differences with ∆ x = 0.1 and 0.01 m, C fl = 0.5 and 0.99 (at least one of these should be unstable). E. Use 1 st order Euler time step instead of L-F with C fl =0.5, ∆ x = 0.1 m, to see if an instability is present. Plot the results (e.g. ., with Tecplot). See the example Code distributed by email....
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