Benchmarking Against Analytical 2D Dispersion Models
POLLUTEv10 Example 13 provides another important model validation case, comparing numerical results from POLLUTEv10 with the analytical solution implemented in TDAST, developed by P. Javandel and colleagues in 1984.
This example focuses on 2-dimensional plane dispersion in an infinitely deep porous medium, offering insight into plume spreading under uniform flow conditions.
Problem Overview
The simulation considers:
- A conservative contaminant (no sorption)
- A constant source concentration
- Uniform groundwater flow
- 2D dispersion in an infinite domain
Key Conditions
- Source concentration (co) = 1.0 g/L
- Time of interest = 4 years
- Flow is steady and uniform
Conceptual Model
The system represents:
- An infinitely thick porous medium
- A continuous source releasing contaminant
- Transport governed by advection and diffusion
Although the domain is infinite:
- Results are evaluated over the top 10 m for comparison
Input Parameters
| Property | Value | Units |
|---|---|---|
| Darcy Velocity (va) | 1.0 | m/a |
| Diffusion Coefficient (D) | 0.01 | m²/a |
| Distribution Coefficient | 0.0 | cm³/g |
| Soil Porosity (n) | 1.0 | – |
| Dry Density | 0.0 | g/cm³ |
| Soil Thickness (H) | 10.0 | m |
| Sub-layers | 20 | – |
| Source Concentration | 1.0 | g/L |
| Time of Interest | 4 | years |
Transport Processes
1. Advection
- Driven by constant Darcy velocity (1 m/a)
- Controls plume movement direction
2. Diffusion / Dispersion
- Causes plume spreading in all directions
- Governed by D = 0.01 m²/a
3. No Sorption
- Conservative contaminant
- No retardation effects
Analytical Comparison (TDAST)
The TDAST model provides an analytical solution for:
- 2D plane dispersion
- Infinite domain conditions
- Uniform flow fields
Purpose of Comparison
- Validate POLLUTEv10 numerical accuracy
- Ensure correct implementation of dispersion processes
- Benchmark plume geometry and concentration distribution
Graphical Output: Depth vs Concentration
PDF Report
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Open in new tab Key Insights
- Analytical solutions remain essential for model verification
- 2D dispersion produces predictable plume geometries
- Infinite domain assumptions simplify boundary effects
- POLLUTEv10 can accurately simulate multi-dimensional transport
Importance of Discretization
- 20 sub-layers used for vertical resolution
- Adequate for capturing concentration gradients over 10 m
Increasing sub-layers improves resolution for sharper gradients or shorter time scales
Practical Applications
This example is relevant for:
- Groundwater contamination assessments
- Plume migration prediction
- Model calibration and validation
- Regulatory and environmental studies
Conclusion
POLLUTEv10 Example 13 demonstrates the model’s capability to accurately reproduce 2D contaminant transport behavior and match analytical solutions such as TDAST.
Key takeaways:
- Advection controls plume direction
- Diffusion governs plume spreading
- Analytical comparisons build confidence in model results
This example reinforces POLLUTEv10 as a reliable tool for groundwater contaminant transport modeling.