Numerical Dispersion Problem

(ADVANCED – Numerical aspects)

Real-world contaminant transport problems are complex beyond the assumptions of analytical solutions, so numerical solutions of the transport equation are often utilized. But when comparing simple numerical solutions to exact analytical solution, an extra dispersion (or spreading) of the contaminants is observed. This is called numerical dispersion or ‘numerical dilution’.

Conduct the following exercise to better understand numerical dispersion and how to minimize it.

• Create a simple synthetic numerical model using MAGNET of two-dimensional groundwater flow between two rivers separated by 100m and with a relative stage difference of 1m (see diagram below). The aquifer is approximately 20m thick and has a hydraulic conductivity of 10 m/d.
• Place a concentration plume source (instantaneous) at the position indicated in the diagram.
• Also place a zone of particles at the position indicated in the diagram.
• Simulate particle tracking and concentration plume migration, accounting only for advection. Use default grid settings.
• Comment on any differences you see. Explain which feature (particle or concentration plume) represents the exact solution. Interpret why numerical dilution happens.
• Perform sensitivity analysis with respect to grid size (NX) and time-step (∆t). Explain how numerical dilution can be minimized.