## ES 105 Homework: January 30, 2009

Below you will find the discussion and relevant materials for the ES 105 homework assignment due on January 30, 2009.

## Plots

Please consult the main Fortran source code for details. Basically, the amplitude was calculated as before in HW#2 using hte Elliptic equation. The Parabolic equation was solved using the Crank-Nicholson scheme with the following parameters: r = 0.75; q = 0.999; RMSE = 0.001; h =k = L/35; Dt = 137.76. RMSE was calculated between the steady state concentration values and the transient concentration values. The spectral radius was also calculated between each time step as it approached 1. Other parameters used in this calculation were: L(Length)=150*E+3; Total # of Nodes = 3780; Half Bandwidth (NHB) = 105; N+1=36 (# of nodes in Y direction); 3*N=105 (# of nodes in X direction); w = 1.41*E-4; t = 20.0*E-5/Height;

Amplitude, Status quo

(H1=20,H2=3,H3=20)

Amplitude, Status quo

(H1=20,H2=3,H3=20)

Concentration,Status quo

(H1=20,H2=3,H3=20)

Concentration,Status quo

(H1=20,H2=3,H3=20)

Sedimentation Rate: Hot Spot and Cold Spot

(H1=20,H2=3,H3=20)

(HOT SPOT= +1.0727*E-5; COLD SPOT= -1.1243*E-4)

(H1=20,H2=3,H3=20)

(H1=20,H2=3,H3=20)

Overlay of Transient Results vs. Steady State Results

(H1=20,H2=3,H3=20)

Hot Spot

Half-life~0.2 (used the following data: hot & cold)

Cold Spot

Half-life~0.3

Thanks to Amir for help and suggestions.