## Peclet number = 99999?

A discussion forum for Hydrus-1D users.
ckanno
Posts: 2
Joined: Thu Mar 24, 2016 12:38 am
Location: USA

### Peclet number = 99999?

Hi,

I am using HYDRUS 1D to run simple "pulse" simulations. Some small amount of water and solute enters through the top of the domain and I'm interested in the solute concentration in space and time (particularly at the bottom of the domain). I have attached two example run files. Here are some details about the set-up:
Geometry: 3 m homogeneous sandy loam, uniform grid spacing (0.003 m)
Initial conditions: Hydrostatic and no solute originally in the profile
Upper Boundary Variable flux condition: Water flux (with solute) equal to the soil hydraulic conductivity for a short period of time, then set to 0 for the rest of the simulation
Lower boundary condition: Pressure head = 0
Solute upper boundary condition: concentration flux
Solute lower boundary condition: zero concentration gradient
Solute solution scheme: Crank Nicholson & Galerkin finite element
Solute transport: Dispersivity = 0.1 m, linear partitioning into soil and air phases, aqueous degradation rate
Max time step = 0.01 hr

When I look at the run time information output for these simulations, the "example" simulation (with a top boundary nonzero flux for a very short period of time) reports a Peclet number of 99999 for the entire simulation. In "example2" (which has a top boundary nonzero flux for a longer period of time) the Peclet number is 99999 for the first 1000 hrs then drops to <0.05 for the rest of the simulation. This 99999 Peclet number is concerning. It seems like a NaN or a placeholder.

I have a couple of questions:
1) Is this 99999 Peclet number an actual value calculated by the model or is it a NaN or placeholder for when the value is too small or too large?
2) If the Peclet number is indeed 99999, do you have any suggestions on what I should tweak to get a more reasonable result?

-Cynthia
Attachments
Forum Example Files.zip
Example and Example 2 files discussed in post. I did not include the full output file to meet upload requirements (may need to run for the full time to see what I'm talking about)

Posts: 30
Joined: Wed Sep 30, 2015 5:04 am
Location: Israel

### Re: Peclet number = 99999?

Hi Cynthia,
I would reduce the dispersion to 0.003 to accommodate the small cells you set.
However, I run example2 with various alterations, without sorting the Peclet number issue.

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Jirka
Posts: 4759
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

### Re: Peclet number = 99999?

Peclet number is defines as: q*dx/theta/D
Dispersion coefficient is defined as: q*dispersivity+diffusion.

If you have diffusion equal to zero (which I assume you have), and zero flux, then the dispersion coefficient is equal to zero and the Peclet number is undefined/infinity. HYDRUS then instead prints 99999.

J.

Posts: 30
Joined: Wed Sep 30, 2015 5:04 am
Location: Israel

### Re: Peclet number = 99999?

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ckanno
Posts: 2
Joined: Thu Mar 24, 2016 12:38 am
Location: USA

### Re: Peclet number = 99999?

Thank you both for your help!

Mitra
Posts: 9
Joined: Thu Dec 06, 2018 3:44 pm
Location: Switzerland

### Re: Peclet number = 99999?

peclet number is defined as ''Maximum local Peclet number'' in the manual, does it mean that peclet number at each time step is calculated based on the maximum flux in the entire domain? Also, I was wondering if you would have some suggestions for me to calculate the peclet number averaged over the entire domain for each time step/ for the enire simulation time.

Thanks.

Jirka
Posts: 4759
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

### Re: Peclet number = 99999?

The Peclet number (see the formula in the manual) is calculated at each time step for all elements using local values of dispersion, flux, water content, and element size, and the maximum number of all elements is reported in the Run_inf.out file. I guess you can as well calculate the profile Peclet number using average values of these variables and the profile depth.

For steady-state flow conditions, this should be trivial. For transient flow conditions, you will have to make some decision on how to average various values.

J.