Tutorial 3.04

Tutorial 3.04

Flow and transport in a transect to a stream

The most complicated fourth example considers water flow and solute transport in a vertical transect with a stream. The transport domain is relatively complex and consists of objects formed by polylines and splines. The problem, divided into three parts, also demonstrates how results of a previous simulation can be used in follow-up calculations with different boundary conditions or having additional features. At first (A), steady state water flow in the transect towards the stream is calculated. Second (B), a source (e.g., simulating water drainage from waste disposal site) is added to the soil surface about 30 m to the left of the stream for a duration of 100 d. Finally (C), the contaminant source is assumed to be removed after 100 days. Transport of the 100-day solute pulse through the unsaturated zone into groundwater and to the stream is subsequently followed for 1100 days.

1. Steady-state water flow
    
2. Water and contaminant source at the surface
    
3. Plume movement towards a stream
    
4. Additional modification - loosing and gaining stream

We believe that by carrying out these four examples, HYDRUS users will obtain the basic skills necessary to solve their own two-dimensional problems. We wish you all the luck and patience needed in this endeavor.

Download the PDF file with detailed description accompanied with figures.

1. Water Flow to a Stream 1

Video for Version 1.0 (52 MB) - Download
Download Project Plume1x.zip (0,6 MB)

• Project Manager (File->Project Manager)
  Button “New”

• New Project (or File->New Project)
  Name: Plume1
  Description: Water flow to a stream - 1
  Working Directory: Temporary – is deleted after closing the project
  Button “Next”

• Domain Type and Units (Edit->Domain Geometry->Domain Type and Units)
  Type of Geometry: 2D - General
  2D-Domain Options: 2D - Vertical Plane XZ
  Units: cm
  Uncheck "Edit domain properties, initial and boundary conditions on geometric objects"
  Initial Workspace: Xmin=-100 cm, Xmax=5100 cm, Zmin=-50 cm, Zmax=550 cm (to accommodate the transport domain)
  Button “Next”

• Main Processes (Edit->Flow and Transport Parameters->Main Processes)
  Check Box: Water Flow
  Button “Next”

• Time Information (Edit->Flow and Transport Parameters->Time Information)
  Time Units: days
  Final Time: 100
  Initial Time Step: 0.0001
  Minimum Time Step: 0.00001
  Maximum Time Step: 5
  Button “Next”

• Output Information (Edit->Flow and Transport Parameters->Output Information)
  Print Options:
  Check T-Level Information
  Check Screen Output
  Check Press Enter at the End
  Print Times: Count: 6
  Update
  Print Times: 1 5 10 25 50 100
  Button “Next”

• Water Flow - Iteration Criteria (Edit->Flow and Transport Parameters->Water Flow Parameters->Iteration Criteria )
  Leave default values as follows:
  Maximum Number of Iterations: 10
  Water Content Tolerance: 0.001
  Pressure Head Tolerance: 1
  Lower Optimal Iteration Range: 3
  Upper Optimal Iteration Range: 7
  Lower Time Step Multiplication Factor: 1.3
  Upper Time Step Multiplication Factor: 0.7
  Lower Limit of the Tension Interval: 0.0001
  Upper Limit of the Tension Interval: 10000
  Initial Condition: In Pressure Heads
  Button “Next”

• Water Flow - Soil Hydraulic Model (Edit->Flow and Transport Parameters->Water Flow Parameters->Hydraulic Properties Model)
  Radio button - van Genuchten-Mualem
  Radio button - No hysteresis
  Button “Next”

• Water Flow - Soil Hydraulic Parameters (Edit->Flow and Transport Parameters->Water Flow Parameters->Soil Hydraulic Parameters)
  Leave default values for loam
  Explore Catalog of Soil Hydraulic Properties and Neural Network Predictions
  Button “Next”

• FE-Mesh - FE-Mesh Parameters (Edit->FE-Mesh->FE-Mesh Parameters)
  Tab Main: Targeted FE – Size – Unselect Automatic and specify TS = 25 cm
  Tab Stretching: Stretching Factor = 3; Stretching direction = X - direction
  Button “OK”

• Definition of the Transport Geometry Click on Grid and Work Plane Setting at the Toolbar (or Tools->Grid and Work Plane)
  Grid Point Spacing – Distance w = 100 cm, Distance h = 20 cm
  Make sure that Snap to Grid is checked
   

• Define Outer Boundary
  Select the Line-Polyline command from the Edit Bar (or Insert->Domain Geometry->Curves->Polylines->Graphically) and define left, bottom and right boundaries of the transport domain as displayed in the figure below
  Select the Spline command from the Edit Bar (or Insert->Domain Geometry->Curves->Splines->Graphically) and define the upper boundary of the transport domain as displayed in the figure below.
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  Notice that units in this figure are in meters, and thus have to be converted to cm.

• Define the Planar Surface
  Select the Planar Surface via Boundaries command from the Edit Bar (or Insert->Domain Geometry->Surfaces->Planar->Graphically) and click at the outer boundary.
  Alternatively, you can use the Planar Surfaces - Generate command from the Edit Bar to generate the Planar Surface automatically.

• Define FE-Mesh
  Click on the FE-Mesh Tab under the View Window.
  Select the Insert Mesh Refinement command from the Edit Bar (or Insert->FE-Mesh Refinement->Graphically): a dialog New FE Mesh Refinement appears. Here select Line - FE-Size and specify Finite Element Size S=10 cm.
  After clicking OK, select the top boundary of the transport domain.
  Click Generate FE-Mesh from the Edit Bar (or Edit->FE-Mesh->Generate FE-Mesh)
  Click on View All at the toolbar (or View->View All)

• Water Flow Initial Conditions:
  Click on the Initial Conditions Tab under the View Window.
  Or on the Navigator Bar click on Initial Conditions – Pressure Head (or Insert->Initial Conditions->Pressure Head)
  a) Select the entire transport domain between x=0 cm and 4700 cm.
  Click on the Set Pressure Head IC command at the Edit Bar, check Equilibrium from the lowest located nodal point, set equal to 400 cm (Bottom Pressure Head Value), and check Slope in the x-direction = -2.8o.
  b) Select the entire transport domain between x=4600 cm and 5000 cm.
  Click on the Set Pressure Head IC command at the Edit Bar, check Equilibrium from the lowest located nodal point, set equal to 175 cm (Bottom Pressure Head Value), and check Slope in the x-direction = 2.4o.

• Water Flow Boundary Conditions:
  Click on the Boundary Conditions Tab under the View Window.
  Or on the Navigator Bar click on Boundary Conditions – Water Flow (or Insert->Boundary Conditions->Constant Head)
  a) Select Constant Head from the Edit Bar, select the left side boundary, and specify 400 cm with Equilibrium from the lowest located nodal point.
  b) Select Constant Head from the Edit Bar, select the right side boundary, and specify 190 cm with Equilibrium from the lowest located nodal point.
  c) Zoom on the stream. Select Constant Head from the Edit Bar, select all nodes with the z-coordinate smaller than 175 cm, and specify 80 cm with Equilibrium from the lowest located nodal point.
  d) Zoom on the slope left of the stream. Select Seepage Face from the Edit Bar and select all nodes with the z-coordinate smaller than 300 cm.
  Click on View All at the Toolbar (or View->View All).

• Save
  Save the project using the Save command on the Toolbar (or File->Save).

• Run Calculations
  Click the Calculate Current Project command on the Toolbar (or Calculation->Calculate Current Project)
  (Execution time on 3 GHz PC – 10 s)
• OUTPUT:

Results – Graphical Display: Pressure Heads (from the Navigator Bar, or Results->Display Quantity->Pressure Heads from menu)
Use Listbox Time Layer or Slidebar on the Edit Bar to view results for different print times
Check Flow Animation
Select different display modes using Options->Graph Type

Results – Graphical Display: Velocity Vectors (from the Navigator Bar, or Results->Display Quantity->Velocity Vectorss from menu)

2. Water Flow and Solute Transport to a Stream 2

Video for Version 1.0 (26 MB) - Download
Download Project Plume2x.zip (0,6 MB)

Add the source at the soil surface

Close the Plume1 Project (click Save Project at the Toolbar or File->Save)

• Project Manager (File->Project Manager)
  Select the Plume1 project
  Button “Copy”
  Name: Plume2
  Description: Water flow and solute transport to a stream - 2
  Button “OK”

• Main Processes (Edit->Flow and Transport Parameters->Main Processes)
  Check Box: Solute Transport
  Button “OK”

• Solute Transport - General Information (Edit->Flow and Transport Parameters->Solute Transport Parameters->General Information)
  Select GFE with artificial dispersion
  Button “Next”

• Solute Transport - Transport Parameters (Edit->Flow and Transport Parameters->Solute Transport Parameters-> Solute Transport Parameters)
  Molecular Diffusion Coefficient for Liquid Phase, Diffus. W. = 3 cm2/d
  Longitudinal Dispersivity, Disp.L = 10 cm
  Transverse Dispersivity, Disp.T = 1 cm
  Button “Next”

• Solute Transport - Reaction Parameters (Edit->Flow and Transport Parameters->Solute Transport Parameters-> Solute Reaction Parameters)
  CBound1=0 (this is concentration for inflow from the left and right side of the transport domain)
  Cbound2=1 (this is concentration for inflow from the source at the surface)
  Button “Next”

• Water Flow Initial Condition:
  Import the final pressure head profile from Plume1 as the initial condition for Plume2 (Edit->Initial Conditions->Import)
  Find project Plume1
  Select Pressure Head and click OK.

• Water Flow and Solute Transport Boundary Conditions: Click on the Boundary Conditions Tab under the View Window.
  a) Zoom on the soil surface with x=16-17 m.
  Select Constant Head from the Edit Bar, select the top four nodes between x=16 and 17 m, and specify h=0 cm.
  b) On the Navigator Bar click on Boundary Conditions – Solute Transport.
  Select Third-Type from the Edit Bar, select the top nodes between x=16 and 17 m, specify Pointer to the Vector of Boundary Conditions = 2.
  Click on View All at the toolbar (or View->View All)

• Save
  Save the project using the Save command on the Toolbar (or File->Save).

• Run Calculations
  Click the Calculate Current Project command on the Toolbar (or Calculation->Calculate Current Project)
  (Execution time on 3 GHz PC – 50 s)
• OUTPUT:

Results – Graphical Display: Pressure Heads (from the Navigator Bar, or Results->Display Quantity->Pressure Heads from menu)
Use Listbox Time Layer or Slidebar on the Edit Bar to view results for different print times
Check Flow Animation
Select different display modes using Options->Graph Type

Results – Graphical Display: Concentrations (from the Navigator Bar, or Results->Display Quantity->Concentrations from menu)
Click with the right mouse button on the color scale and from the pop-up menu click on Min/Max Global in Time. See how the display changed.

Results – Other Information: Solute Fluxes (from the Navigator Bar, or Results->Boundary Information->Solute Fluxes from menu)
Constant Boundary Flux

3. Water Flow and Solute Transport to a Stream 3

Video for Version 1.0 (34 MB) - Download
Download Project Plume3x.zip (0,6 MB)

Change boundary condition after 100 d of simulation

Close the Plume2 Project (click Save Project at the Toolbar or File->Save)

• Project Manager (File->Project Manager)
  Select the Plume2 project
  Button “Copy”
  Name: Plume3
  Description: Water flow and solute transport to a stream - 3
  Button “OK”

• Time Information (Edit->Flow and Transport Parameters->Time Information)
  Time Units: days
  Initial time: 100
  Final time: 1200
  Initial Time Step: 0.001
  Minimum Time Step: 0.00001
  Maximum Time Step: 50
  Button “Next”

• Output Information (Edit->Flow and Transport Parameters->Output Information)
  Print Options:
  Check T-Level Information
  Check Screen Output
  Check Press Enter at the End
  Print Times: Count: 11
  Update
  Default
  Button “Next”

• Water Flow and Solute Transport Initial Condition:
  Import the final pressure head profile from Plume2 as the initial condition for Plume3 (Edit->Initial Conditions->Import)
  Find project Plume2
  Select Pressure Head and Concentrations and click OK
   

• Water Flow and Solute Transport Boundary Conditions:
  Click on the Boundary Conditions Tab under the View Window or on the Navigator Bar click on Boundary Conditions – Water Flow.
  Select Constant Flux from the Edit bar and assigned it to all nodes at the soil surface between the seepage face and the left side, and between the stream and the right side; and specify a flux=0.05 cm/d.

• Observation Nodes
  Click on the Domain Properties Tab under the View Window.
  On the Navigator Bar click on Domain Properties – Observation Nodes (or Insert->Domain Properties->Observation Nodes).
  Click on Insert Observation Node command at the Edit Bar and specify 5 points arbitrarily between the source and the stream.

• Save
  Save the project using the Save command on the Toolbar (or File->Save).

• Run Calculations
  Click the Calculate Current Project command on the Toolbar (or Calculation->Calculate Current Project)
  (Execution time on 3 GHz PC – 195 s)

• OUTPUT:
  Click on the Results Tab under the View Window. Menu: Post-Processing ->Observation Points: Concentrations
  Menu: Post-Processing ->Time Information: Peclet Numbers
  Menu: Post-Processing ->Boundary Information->Solute Fluxes: Constant Boundary Flux
  Menu: Post-Processing ->Mass Balances Information
  Menu: Post-Processing -> Graphical Display of Results
  Concentrations

4. Additional Modification - Loosing and Gaining Stream

Two additional modifications of the above tutorial are presented in this section. In the first run, we simulate a sudden flooding of an initially dry stream. In the second run, we simulate the time-variable water levels (increasing and decreasing) in the stream.

1. Sudden flooding of an initially dry stream
2. Time-variable water level in a stream (a gaining and/or loosing stream)

Download tutorial document: PDF (0.22 MB)
Download tutorial projects: h3d2 Zip (2.4 MB)