Mathematically, there is a difference between transfer B.C.'s for 2D and 3D models:
In a 3D model, the exchange area of a river is defined either on slice faces (in most cases orientated more or less horizontally), or join faces (vertical) between two slices.
In 2D, the transfer area can only be regarded as a 1D line, due to reducing the system by one dimension. (For theoretical background: The vertically avaraged equations for 2D problems according to Dupuit are being introduced in chapter 1 and 2 of the FEFLOW reference manual.)
From a practical point of view, there is no z-dimension and consequently there are no velocity components in z-direction either.
Any transfer boundaries in 2D models on slice faces can only consist of element edges. Note that any refinement of such elements yields new element edges, possibly resulting in unwanted additional exchange rates! See also the attached picture.
There is a difference between edges at outer boundary of a model and edges located inside the model: For outer edges, there is only one adjacent element, while for inner edges there are two adjacent elements. In the latter case, the length of the edge (2D) or area of the face (3D) is taken twice. At all outer boundaries, the length or face is only taken once.
Looking at the physical units, the resulting exchange rate is [L³/T], L = length, T = time.
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[li]In [u]2D horizontal confined models[/u], this amount results from the difference in the potential between surface water and groundwater [L] * the edge length [L] * the transfer rate [L/T].
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[li]In [u]2D horizontal unconfined models[/u] the exchange rate results from the potential difference [L] * edge length [L] * saturated thickness [L] * transfer rate [1/T]. The saturated thickness is being calculated by the difference between calculated groundwater surface elevation [L] and the elemental distribution of the parameter "Bottom elevation" [L].
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In [u]2D horizontal unconfined models[/u] or models with the 'free' mode (3D), one can also work with [b]depth integrated conditions[/b]. The boundary flow at fluid-flux boundary conditions is highly interlinked with the hydraulic head (groundwater level) inside the model. In some cases during the iterative solution process or over time in transient models, it may happen that a slightly lower hydraulic head leads to less inflow and vice versa, so that finally no inflow is left and the model becomes dry. For such cases, FEFLOW provides the Fluid-flux BC as Integral BC. In this boundary-condition type, the saturated thickness is not changed during the model run. In 2D models, the input values for the boundary condition are depth-integrated flux values. In the 3D 'free' mode, the model uses the original layer stratigraphy for the calculation of the boundary-condition area, no matter what the current water level is.
When a so called integral transfer BC is applied, the exchange rate is obtained from the potential difference [L] * edge length [L] * integral of transfer rate [1/T] over depth [L].
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In [u]3D models[/u], depth integrated transfer boundary conditions become only effective when using the 'free'
mode. In all 3D modes, the transfer rate is calculated from potential difference [L] * face area [L²] * transfer rate [1/T].
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Note: In 2D horizontal cases, when using either the confined approach or the unconfined approach with integral transfer boundary conditions, the transfer rate parameters as specified must incorporate the desired depth.
For many practical cases, it is needed to calculate a transfer rate (or leakage amount) between groundwater and surface water by an exchange area orientated horizontally (lakes, shallow ditches, ponds...) or even a combination of both (canals, drains). Since the 2D approach does not take any z-components into account, it is highly advisable to work with a 3D model in this case. In a vertically, essentially homogenous exchange situation (e.g. a narrow, yet deep creek) where the z-components can be neglected, a 2D approach might be sufficient.
