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Comparison of Finite Difference Method, Philips Method and GreenAmpt Model in Infiltration Simulatio

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Mathematical Methods have been developed for computing and ... Figure 2. Wetting front of Philips method using different WC for the upper boundary condition ... – PowerPoint PPT presentation

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Title: Comparison of Finite Difference Method, Philips Method and GreenAmpt Model in Infiltration Simulatio


1
Agron 677 Term Project
Comparison of Finite Difference Method, Philips
Method and Green-Ampt Model in Infiltration
Simulation Zhiming Qi Department of Ag
Engineering
2
Outline
  • Introduction
  • Materials and Methods
  • Results and Discussion
  • Conclusion
  • Suggestion

3
Introduction
  • Infiltration is a key component to hydrological
    process.
  • Mathematical Methods have been developed for
    computing and simulating infiltration
  • Green-Ampt Model (1911)
  • Philips method for Richards equation
    (1957)
  • Finite difference method for Richards
    equation
  • Boundary Conditions
  • First class boundary constant WC
    upper boundary WC c
  • Second class boundary constant
    water influx q c
  • 2nd boundary in most
    natural infiltration process
  • Third class boundary constant
    change of water influx dq/dt c
  • Computer Models have been developed to simulate
    the infiltration procedure.
  • DRAINMON (Green-Ampt)
  • MIKE-SHE and HYDRUS (Richards,
    Finite difference method)

4
Introduction
  • Mathematical Methods for infiltration Modeling
  • 1. Green-Ampt Model (1911)

Green-Ampt model calculates cumulative
infiltration by assuming water flow into a
vertical soil profile like a piston flow (first
boundary condition)
by Chow et al. (1988)
Parameters required
K
5
Introduction
  • Mathematical Methods for infiltration Modeling
  • 2. Finite difference method for Richards
    equation
  • Explicit scheme
  • Implicit scheme
  • Crank-Nicolson scheme
  • (any boundary conditions)


http//hydram.epfl.chf
Parameters required
6
Introduction
  • Mathematical Methods for infiltration Modeling
  • Philips method for Richards equation
    (1957)
  • (only for first boundary
    condition)


Parameters required
.
7
Materials and Methods
from Haverkamp et al. (1977).
  • Soil
  • Boundary Condition (2nd)

8
Materials and Methods
  • Parameters for Green-Ampt Model

K
Parameters required
Initial estimation
0.287-0.10 0.187 cm3/cm3
9
Materials and Methods
  • Mathematical Method for Green-Ampt Model

Newtons Iteration for the equation after ponding
http//www.krellinst.org/
10
Materials and Methods
  • Parameters for Implicit Finite Difference
    (Richards)

Parameters required
are known
  • Parameters for Philip Method (Richards)

Parameters required
11
Materials and Methods
  • Evaluation Criteria

Cumulative Infiltration (Mass Balance)
Percentage Error
Model Efficiency
Program running time
Wetting Front
Wetting front plotting
12
Results and Discussion
  • Implicit Finite Method

PE 0.964 Running Time 8 min
Figure 1. Wetting front by finite difference
method for Richards equation.
13
Results and Discussion
  • Philips Method

0.287
PE 160 Running Time lt 2 sec.
Figure 2. Wetting front of Philips method using
different WC for the upper boundary condition
14
Results and Discussion
  • Philips Method

0.287
PE 160 Running Time lt 2 sec.
Figure 2. Wetting front of Philips method using
different WC for the upper boundary condition
15
Results and Discussion
  • Philips Method

0.287
0.265
PE 14.5 Running Time lt 2 sec.
PE 160 Running Time lt 2 sec.
Figure 2. Wetting front of Philips method using
different WC for the upper boundary condition
16
Results and Discussion
  • Philips Method

0.287
0.265
PE 14.5 Running Time lt 2 sec.
PE 160 Running Time lt 2 sec.
Figure 2. Wetting front of Philips method using
different WC for the upper boundary condition
17
Results and Discussion
  • Philips Method

0.287
0.265
0.260
PE 14.5 Running Time lt 2 sec.
PE -0.57 Running Time lt 2 sec.
PE 160 Running Time lt 2 sec.
Figure 2. Wetting front of Philips method using
different WC for the upper boundary condition
18
Results and Discussion
  • Philip Method Parameters

Figure 3. Parameters of Philip method
19
Results and Discussion
  • Green-Ampt Method

0.287
0.265
PE 0.20 Running Time lt 2 sec.
PE 0.19 Running Time lt 2 sec.
Figure 4. Wetting front from Green-Ampt model
20
Results and Discussion
  • Comparison


0.1 Hour
Figure 6. Wetting fronts from finite difference,
Philip methods and Green-Ampt model
21
Results and Discussion
  • Comparison


0.4 Hour
0.1 Hour
Figure 6. Wetting fronts from finite difference,
Philip methods and Green-Ampt model
22
Results and Discussion
  • Comparison

0.7 Hour
0.4 Hour
0.1 Hour
Figure 6. Wetting fronts from finite difference,
Philip methods and Green-Ampt model
23
Results and Discussion
  • Comparison

Table 1. Models strength and drawback
for infiltration
simulation under the 2nd class boundary condition

24
Conclusion
  • All the models could show high accuracies in
    simulating cumulative infiltration.
  • Finite difference method
  • best wetting front prediction
  • treat the second class boundary best among
    the 3 models
  • but sometimes numerically unstable
  • Green-Ampt model
  • required least parameters and the simplest
    programming
  • but the wetting front is not precise
  • Philips method
  • solve Richards equation much quicker than
    finite difference method
  • high numerical stability
  • but care should be taken under 2nd boundary
    condition
  • programming is much complicated

25
Suggestion
  • Finite difference method is the best approach for
    cumulative infiltration and wetting front
    prediction
  • Philips method is a good alternative for finite
    difference method if there is a problem in
    numerical stability for finite difference method
    or a good computer is not accessible.
  • Green-Ampt model is a simple and good method if
    only the cumulative infiltration is concerned.

26
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