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Unformatted text preview: MAE 290B, Winter 2010 HOMEWORK 5 Due Wed 03-03-2010 in class Provide source codes used to solve all problems PROBLEM 1 Integrate numerically Burgers equation ∂ t u + u∂ x u = ν∂ xx u, in the domain- π ≤ x < π with periodic boundary conditions and initial conditions u ( x,t = 0) = exp(- x 4 ). 1. Solve for ν = 10- 3 using N = 32 , 256 grid points in x . (a) Use a Lerat scheme with α = 1 / 2 and β = 1 / 2 (Lax-Wendroff scheme). For each N determine the maximum value of Δ t max for which this scheme is stable and integrate with Δ t = Δ t max / 5. (b) Use a Lerat scheme with α = 1 / 2 and β = 1 (MacCormack scheme). Use the same Δ t as above. (c) Use a Fourier spectral discretization and a RK3- θ scheme with the same Δ t as above. 2. Compare the solutions to the problem at t = 3. Interpret the differences between these solutions in terms of the properties of each spatial discretization scheme. Which solution should be considered more reliable?...
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This note was uploaded on 09/22/2010 for the course MAE MAE290B taught by Professor Mae290b during the Spring '10 term at UCSD.
- Spring '10