ce5504 – surface water quality modeling ce5504 surface water quality modeling lab 1. numerical...
Post on 19-Dec-2015
220 views
TRANSCRIPT
CE5504 – Surface Water Quality Modeling
CE5504 Surface Water Quality Modeling
Lab 1. Numerical Methods and Population Growth Modeling
dcVdt
dc
Vdt
Begin with a mass balance on microbial growth
CE5504 – Surface Water Quality Modeling
in
dXV Q X Q X Reactiondt
dXV V k Xdt
dXk X
dt
(Mihelcic 1999, Figure 5.4)
Exponential growth model
CE5504 – Surface Water Quality Modeling
dXX
dt
( )0
ttX X e
( )0
ttX X e
Logistic growth model
CE5504 – Surface Water Quality Modeling
max 1dX X
Xdt K
max0
0
1t
t
KX
K Xe
X
(Mihelcic 1999, Figure 5.7)
Putting It All Together
CE5504 – Surface Water Quality Modeling
max
max
1
11
ds
ds
dX X Sk X
dt K K S
dS X Sk X
dt Y K K S
(Mihelcic 1999, Figure 5.10)
Numerical Integration
CE5504 – Surface Water Quality Modeling
non-idealized loading functions
variable parameters
multi-segment systems
non-linear kinetics
Code
CE5504 – Surface Water Quality Modeling
max0For t to t
dX X dt
X X dX
Next t
max0For t to t Step dt
dX X dt
X X dX
Next t
Code (continued)
CE5504 – Surface Water Quality Modeling
max0
,
For t to t Step dt
dX X dt
X X dX
Print t X
Next t