1 / 21

CE5504 – Surface Water Quality Modeling

CE5504 Surface Water Quality Modeling. Lab 2. Numerical Methods and Population Growth Modeling. CE5504 – Surface Water Quality Modeling. Begin with a mass balance on microbial growth. CE5504 – Surface Water Quality Modeling. Exponential growth model. (Mihelcic 1999, Figure 5.4).

zinna
Download Presentation

CE5504 – Surface Water Quality Modeling

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CE5504 Surface Water Quality Modeling Lab 2. Numerical Methods and Population Growth Modeling CE5504 – Surface Water Quality Modeling

  2. Begin with a mass balance on microbial growth CE5504 – Surface Water Quality Modeling

  3. Exponential growth model (Mihelcic 1999, Figure 5.4) CE5504 – Surface Water Quality Modeling

  4. Environmental Resistance (Mihelcic 1999, Figure 5.5) CE5504 – Surface Water Quality Modeling

  5. Logistic growth model (Mihelcic 1999, Figure 5.7) CE5504 – Surface Water Quality Modeling

  6. Example: carry capacity effects (Mihelcic 1999, Figure 5.6) CE5504 – Surface Water Quality Modeling

  7. Monod Model (Mihelcic 1999, Figure 5.8) CE5504 – Surface Water Quality Modeling

  8. Example: resource competition (Mihelcic 1999, Figure 5.9) CE5504 – Surface Water Quality Modeling

  9. The Yield Coefficient CE5504 – Surface Water Quality Modeling

  10. The Death (Respiration) Coefficient CE5504 – Surface Water Quality Modeling

  11. Putting It All Together (Batch Reactor) (Mihelcic 1999, Figure 5.10) CE5504 – Surface Water Quality Modeling

  12. Putting It All Together (Completely-Mixed Flow Reactor) CE5504 – Surface Water Quality Modeling

  13. Numerical Integration • non-idealized loading functions • variable parameters • multi-segment systems • non-linear kinetics CE5504 – Surface Water Quality Modeling

  14. The Euler Method CE5504 – Surface Water Quality Modeling

  15. The Effect of Step Size (Spain 1982, Figure 5.1) CE5504 – Surface Water Quality Modeling

  16. Code CE5504 – Surface Water Quality Modeling

  17. Code (continued) CE5504 – Surface Water Quality Modeling

  18. Code (continued) CE5504 – Surface Water Quality Modeling

  19. Advanced Numerical Techniques The Heun’s Method For i = 0 To tmax For j = 1 To 1 / dt k1 = mu * x X1 = x + dt * k1 k2 = mu * X1 x = x + (k1 + k2) / 2 * dt Next j Next i CE5504 – Surface Water Quality Modeling

  20. Advanced Numerical Techniques The 4th Order Runge Kutta Method For i = 0 To tmax For j = 1 To 1 / dt k1 = mu * x X1 = x + 0.5 * dt * k1 k2 = mu * X1 X2 = x + 0.5 * dt * k2 k3 = mu * X2 X3 = x + dt * k3 k4 = mu * X3 x = x + (k1 + 2 * k2 + 2 * k3 + k4) / 6 * dt Next j Next i CE5504 – Surface Water Quality Modeling

  21. Advanced Numerical Techniques Error Comparison Error (%)for various values of dt at t = 5 days dt Euler Heun 4th RK 1 98.90 85.81 23.70 0.5 95.35 56.70 3.60 0.1 58.68 5.58 0.01 0.01 9.40 0.07 0.001 0.99 0.001 0.0001 0.10 0.00001 0.02 0.000001 0.001 Error criterion:<=0.01 % CE5504 – Surface Water Quality Modeling

More Related