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Pathline tracing

Pathlines are traced in the horizontal plane using the aquifer discharge vector function in the domain and a numerical tracing procedure outlined in section 26 of Strack (1989). Three-dimensional pathline tracing is done using a finite-difference form of equation 24 in the paper by Strack (1984), which uses three-dimensional flow continuity to approximate the vertical component of pathlines.

Steady vs transient models

For transient models, pathlines are traced through a transient flow field that evolves through the duration of the transient simulation (this is new in release 2016-2; earlier releases traced pathlines through the flow field of the last time step in a transient model). From release 2016-2 on, pathlines in transient models start at the specified start time, and can be traced backward to the beginning of the simulation or forward until the end of the simulation. In steady models, pathlines are traced forward or backward until they either exit the model or until the specified total time is reached.

Crossing inter-domain boundaries

Where pathlines cross inter-domain boundaries, the elevation of the pathline is adjusted so that the fraction of the normal component (perpendicular to the boundary segment) of flow above and below the pathline on each side of the inter-domain boundary match. For example, say you have an inter-domain boundary with one domain on the left and three on the right. If the pathline comes to the boundary from the left with 45% of the normal component of discharge above the pathline and 55% below it, the domain and elevation of the pathline side will be determined so that this 45/55 ratio is preserved on the right side as well. There is typically a jump in the elevation of the pathline as it crosses an inter-domain boundary for the following reasons:

  • The elevations of the domains on left and right do not necessarily match
  • Where there are multiple levels on one side of the boundary, the distributions of the normal components of flow vary from one level to another due to \(K\) and flow field variations
  • The total normal components of flow match only approximately from left to right side (see Fitts (2010)). Anaqsim is not matching these normal components of flow perfectly at every point on the boundary — it is matching the total normal discharge across segments of the boundary perfectly.

When the normal discharge components across an inter-domain boundary are in different directions in different levels (usually where flow is nearly stagnant) this algorithm breaks down, and under such conditions pathlines may terminate at the inter-domain boundary.

Crossing internal linesinks (for example rivers)

When pathlines intersect an internal line-sink boundary such as a river boundary, there are two possibilities: (1) the pathline could be consumed by the linesink and terminate, or (2) the pathline could continue on underneath the linesink. Whether option 1 or 2 occurs is determined based on the elevation of the pathline as it approaches the linesink, the discharge/length of the linesink at the intersection, and the normal component of the domain discharge at the intersection. It is assumed that the linesink is at the top of the domain and draws its water from the upper portion of the domain discharge. If the result is case 2 with the pathline continuing under the linesink, its elevation will generally jump as it crosses under the linesink, gaining elevation if the linesink is extracting water and losing elevation if the linesink is injecting water.

Multi-level models and exits

In multi-level areas of models, pathlines can cross from one level to another vertically. Where pathlines exit the bottom or top of the model due to recharge or leakage (e.g. at the water table for pathlines traced upstream), Anaqsim draws a circle at the end of the pathline and if you move the cursor over the circle, it will display elapsed time, domain, elevation, etc.

Starting points and tracing settings are entered under Pathlines.