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# ComputerProb1 - Aug 29 2006 ATMS 502 CS 505 CSE 566 Jewett...

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1 Aug. 29, 2006 ATMS 502 - CS 505 - CSE 566 Jewett Computer Problem 1 One-Dimensional Linear and Nonlinear Advection Due : beginning of class, 2.5 weeks from now: Thursday, September 14. Your code and plots, printed out - handed in Turn in : Your code, emailed to me w/instructions on how to run it on copper Problem being solved: advection equation Linear case: " u t = # c u x Nonlinear case: u t = # u u x The only difference above is use of c vs. u before u / x . Initial condition: a single sine wave with a wavelength of nx+1 . Boundary condition: periodic; the wave exits the right side of the domain and re-enters the left side (for speed c > 0). Scheme: Lax-Wendroff, with forward time, centered space. The form is: u j n + 1 = u j n " # 2 u j + 1 n " u j " 1 n ( ) + \$ u j + 1 n " 2 u j n + u j " 1 n ( ) where n is the time level, j each of the nx grid points, ν the Courant number, and σ = ν 2 /2 . ν is set to (c t/ x) in the linear case, and (u t/

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ComputerProb1 - Aug 29 2006 ATMS 502 CS 505 CSE 566 Jewett...

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