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N7 Integral modelling approach for flow and reactive transport in groundwater - surface water interaction space

Doctoral student: Tabea Broecker

Supervisors: Prof. Dr. Reinhard Hinkelmann, Prof. Dr. Gunnar Nützmann

Introduction / Background

This research is focused on the hyporheic zone - the transition zone between surface water and groundwater. The hyporheic zone is essential regarding the water balance, the movement of water and the substances transported and transformed therein. Since urban water systems are usually subject to strong human influences, which modify the quality of surface water and groundwater, investigations of the hyporheic zone are important to examine  the retention, transformation and attenuation of harmful solutes. Regarding the complexity of hyporheic exchange processes, numerical models as well as field measurements are helping to get a better understanding of the prevailing processes.


The objective is to develop an integral CFD model in the groundwater-surface water interaction space for flow and transport processes. Most numerical investigations consider the groundwater and surface water as separate environmental compartments. Recently also coupled models were developed. For the integral solver, the three-dimensional Navier-Stokes equations are extended for the use in the porous medium. Flow and transport processes are investigated using a complex turbulence model. The influence of different bed forms (e.g. plain, ripples and dunes) on the exchange are examined. First of all, the approach is developed and validated on a small scale. The results will be compared with laboratory and field measurements as well as with further coupled numerical models. Afterwards, an upscaling approach will be developed.


For all calculations, the free, open source computer fluid dynamics software “OpenFOAM” (Open Field Operation and Manipulation), version 2.4.0, is applied. For the investigation of  groundwater and surface water interactions, an integral solver called „porousInter“, developed by Oxtoby et al. (2013) was validated and will be extended. The solver is based on the two-phase flow solver “interFoam“ and extends the three-dimensional Navier-Stokes equations by the consideration of the porosity and an additional drag and inertia term.


First of all, flow and transport processes at the upper boundary of the hyporheic zone were investigated regarding different ripple geometries and surface hydraulics. For this purpose, the interFoam solver was extended by an advection-diffusion equation. Pressure gradients along the rippled streambed were used to account for hyporheic exchange and showed to be significantly affected by flow velocities, ripples sizes and spaces. A tracer pulse was injected into the surface water. Large parts of the tracer were transported alongside the main stream above the ripples. Due to low velocities and recirculations between the ripples. tracer mass reaching this area was temporarily retained, depending on the ripple geometries and on the flow velocities. The streambed morphology significantly impacts the tracer retention at the surface dead zones and is consequently important for compund movement, exchange and transformations processes within the hyporheic zone.

Initial tracer distribution (top) and tracer distribution after 10 s (center and bottom).


In a further step, the integral solver was tested based on two applications which both compare seepages through a dam with numerical and/or analytical solutions. The two applications confirm that the integral solver produces good results for groundwater-surface water interactions.

Seepages through a homogeneous dam with an impervious foundation for a numerical simulation with the integral solver and two analytical solutions.
Seepages through a rectangular dam with an impervious foundation for three numerical and two analytical solutions.


Based on the second test case (rectangular dam) a parameter study, focusing on the influence of porosity and median grain size, was investigated. The results show that these parameters only slightly affect the water levels, but significantly influence the flow velocities and the computation time.


Aitchison, J. (1972). Numerical Treatment of a Singularity in a Free Boundary Problem. Proceedings of the Royal Society of London, Series A,. 330, 1583, pp. 573–580.

Casagrande, A. (1937). Seepage through Dams. Journal of the New England Water Works Association. 51, 2, pp. 131-170

Oxtoby, O.F., Heyns, J.A. & Suliman, R. (2013). A finite-volume solver for two-fluid flow in heterogeneous porous media based on OpenFOAM: Open Source CFD International Conference, Hamburg, doi: 10.13140/2.1.3075.8400.

Westbrook, D.R. (1985). Analysis of inequality and residual flow procedures and an iterative scheme for free surface seepage. International Journal for Numerical Methods in Engineering. 21, pp. 1791–1802.



Initial project plan

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