Nodal flux reduction by pressure head boundary condition modifier

Figure 1: Simple Drain and Makeup Water box model

This post describes how to use the flux nodal boundary condition modifier: nodal flux reduction by pressure head. This modifier is used when the flux rate is set higher than the available water, which can cause numerical instability and model crashes. By applying the modifier, the flux rate is reduced according to the pressure head, allowing the model to remain stable even when water availability fluctuates. We find this modifier particularly useful when simulating conditions where the water extraction needs to be limited based on available pressure, ensuring more realistic and stable simulations.

For this post we use the same model that we used to demonstrate the simple drain and makeup water boundary conditions (Simple Drain and Makeup Water Boundary Conditions).

The model (see Figure 1) is a simple box model with a depression (pond in the middle). The lateral boundary conditions at x = 0 m and x = 50 m are specified head boundary conditions that fluctuate between 7 and 10 m on a 30-day cycle as follows:

time value table
0      9
30     7
60     10
90     7
120    10
150    7
180    10
210    7
240    10
end

Figure 2: Command description

This range of fluctuation is enough to move water in and out of the depression. In the middle of the depression a flux nodal boundary condition has been assigned with a rate of -2 m3/day. This rate was selected as it exceeds the available amount of water to be pumped during the periods of the simulation where the outer head boundary conditions have a value of 7.

Model Setup:

For this example the simple drain boundary condition has been replaced with a flux nodal boundary condition with the nodal flux reduction by pressure head modifier.

!--------------------- Flux Nodal Boundary Condition
use domain type
surface


clear chosen nodes

choose node
25 0 8

create node set
n_nodalflux

boundary condition 
	type
	flux nodal

	node set
	n_nodalflux

	time value table
	0 -2
	end

    nodal flux reduction by pressure head
    0.01
    0.1 
end

Figure 3: Automatic flux reductions based on pressure head signal

Results:

Figure 3 shows how the flux rate changes over the course of the simulation. When water is available the extraction rate is -2 m3/day, however as the available water decrease (pressure head drops) the rate of water extraction drops, until the pumping stops.

Closing Notes:

1. In the event that you don’t want to use a pressure head specification, a variation of this command exists which controls the flow rate based on total head – nodal flux head constraints

2. When using nodal flux reduction by pressure head it is important that you inspect the reported flux in the water balance file as it may be less than the maximum value specified.