pb3_11 - MPO 662 – Problem Set 3 It is very important...

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Unformatted text preview: MPO 662 – Problem Set 3 It is very important that you discuss the numerical results you produce, particularly if they conform with your expectation about what the solution should look like, and if not what may have caused the problems. Plots with no discussion/commentary are not useful and don’t show us whether you have looked critically at your results. 1 Numerical dispersion 1. Carry out a dispersion analysis for the advection equation u t + cu x = 0 when the spatial derivative is approximated with a fifth-order upwind scheme: u t + c- 2 u j- 3 + 15 u j- 2- 60 u j- 1 + 20 u j + 30 u j +1- 3 u j +2 60Δ x = 0 (1) Plot the dispersion relationship of the real and imaginary part of the frequency as a function of Δ x and contrast it to the dispersion relationship obtained from a second order centered difference scheme. 2. Carry out a dispersion analysis for the advection equation u t + cu x = 0 when a 4-th compact difference scheme is used to compute the special derivative: 1 4 u x |...
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pb3_11 - MPO 662 – Problem Set 3 It is very important...

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