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leendertvanwolfswinkel committed Sep 11, 2024
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8 changes: 4 additions & 4 deletions source/h_1d2d_exchange.rst
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Expand Up @@ -158,10 +158,10 @@ For double connected elements this implies:
Exchange between 1D and groundwater
-----------------------------------

Groundwater interacts with channel and pipes. In 3Di we allow couplings between the 1D and the 2D domain. There are various options that determine the flow, the material of the pipe/channel, the surrounding soil of the groundwater etc. For this 3Di focusses on the large scale effect of the interaction and not on the detailed micro-scale flow. 3Di computes the flux between the two domains based on a diffusive equation, similar to the Darcy equation:
Groundwater (2D domain) can interact with channels and pipes (1D domain). The flow is governed by various parameters: the material of the pipe/channel, the surrounding soil of the groundwater, et cetera. 3Di focuses on the large scale effect of the interaction and not on the detailed micro-scale flow. 3Di computes the flux between the two domains based on a diffusive equation, similar to the Darcy equation:

.. math::
:label: darcy_1d2d
:label: 1D2D groundwater exchange equation
Q_{1D2D} = -A_{1D2D} \kappa_{in/out} \frac{\partial \eta}{\partial \delta}
Expand All @@ -176,11 +176,11 @@ The wet cross-sectional area is based on the length and the wetted perimeter of

.. figure:: image/h_1d2d_groundwaterexchange.png
:figwidth: 400 px
:alt: connected_to_grw
:alt: Sketch of 1D-2D groundwater exchange and the wetted perimeter in red depending on the flow direction.

Sketch of 1D-2D groundwater exchange and the wetted perimeter in red depending on the flow direction.

Each exchange is forced by a water level gradient and scaled by the hydraulic conductivity. Depending on the material, considering pipes or depending on the bed coverage, considering a channel the in and out going flow rates can scale differently. Therefor a in- and a out-going hydraulic conductivity value can be defined. Another scaling factor is the thickness of the pipe or the bed of the channel.
Each exchange is forced by a water level gradient and scaled by the hydraulic conductivity. Depending on the pipe wall material or the channel bed characteristics, the incoming and outgoing flow rates can scale differently. Therefore, an incoming and an outgoing hydraulic conductivity value can be defined. Another scaling factor is the thickness of the pipe or the bed (e.g. the layer of leaves and other non-decomposed organic matter) of the channel.


Breach flow
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14 changes: 4 additions & 10 deletions source/h_subgrid.rst
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Expand Up @@ -13,11 +13,11 @@ Nowadays, detailed bathymetry information becomes more and more available. Howe

Examples of flow in a flume, where a slight change in bathymetry strongly affects the flow.

The key assumption of the subgrid method, is that water levels vary much more gradually, than the bathymetry. In most methods used for hydrodynamic computations, water levels are assumed to be uniform within a computational cell. Traditionally, this is also assumed for the bathymetry within such a cell. The subgrid-based method allows the bathymetry to vary within a computational cell, while the water level remains uniform. In 3Di two grids are defined; a high resolution subgrid and a coarse(r) computational grid.
The key assumption of the subgrid method, is that water levels vary much more gradually than the bathymetry. In most methods used for hydrodynamic computations, water levels are assumed to be uniform within a computational cell. Traditionally, this is also assumed for the bathymetry within such a cell. The subgrid-based method allows the bathymetry to vary within a computational cell, while the water level remains uniform. In 3Di, two grids are defined; a high resolution *subgrid* and a coarser *computational grid*.

All input data, such as the bathymetry, roughness and infiltration rates can be defined on the high resolution grid, while the computations are performed on the coarse computational grid. Volumes and cross-sectional areas are based using the high resolution bathymetry information. The variation of the bathymetry within a computational cell, related to a 2D surface water cell means that a cell can be dry, wet or partly wet.
All input data, such as the bathymetry, roughness and infiltration rates, can be defined on the high resolution grid, while the computations are performed on the coarse computational grid. Volumes and cross-sectional areas are calculated using the high resolution bathymetry information. The variation of the bathymetry within a computational cell, related to a 2D surface water cell means that a cell can be dry, wet or partly wet.

For ground water computational cells, the depth of the impervious layer is assumed to be uniform. The storage capacity in a ground water cell is based on the high resolution bathymetry information. This implies that a ground water cell can also be dry, partly full and maximally filled. This happens when the ground water level reaches the highest level of the bathymetry within a computational cell.
For groundwater computational cells, the depth of the impervious layer is assumed to be uniform. The storage capacity in a groundwater cell is based on the high resolution bathymetry information. This implies that a groundwater cell can also be dry, partly full or completely full. This happens when the groundwater level reaches the highest level of the bathymetry within a computational cell.

The subgrid method has three implications:

Expand All @@ -34,19 +34,13 @@ The subgrid method has three implications:

An example of a computational cell with a bathymetry defined on the subgrid.

Some facts and figures
----------------------

- The use of high resolution information goes hand in hand with large amounts of data. To compress this data, it is stored during the computations in tables. More information about this can be found in :ref:`subgrid_tables`.
- There are more variables defined at the high resolution grid; such as roughness, infiltration capacity and hydraulic connectivity. These will be introduced later in the documentation.
- Users define for the grid generation a cell size (of the finest grid resolution) and the number of refinement layers. A computational cell consists always of an even number of subgrid cells. In addition, the user needs to define where and if refinements should be defined. One can define polygons or lines to indicate these areas and the refinement level.

.. _subgrid_tables:

Subgrid tables
--------------

The high resolution subgrid data is compressed in tables that allow fast access during the simulation. These tables describe the relation between water level and the following variables:
The use of high resolution information also means that more data is used during the simulation. 3Di stores this data in subgrid tables to limit the memory usage and allow fast access during the simulation. These tables describe the relation between water level and the following variables:

* Volumes per computational cell (1D, 2D)
* Cross-sectional area per half of cell face (2D)
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