### Differentiate BC docs for Richards and Transport models

* Specify respective quantities and use cases.
* Add docs on Outflow BC.
parent f8159599
 ... ... @@ -11,6 +11,7 @@ boundary conditions by means of the segment indices. .. contents:: :depth: 3 :local: Boundary Condition File ----------------------- ... ... @@ -27,9 +28,9 @@ of values. This way, the time interval may be limited, or a boundary condition may be interpolated between the specified times. Certain types of boundary conditions may require additional keys. .. code_block:: yaml .. code:: yaml : index: conditions: : ... ... @@ -86,54 +87,101 @@ A boundary condition has the following template: value: # .. object:: Dirichlet .. option:: Dirichlet A Dirichlet boundary conditions determines the exact value of the solution at the boundary. **Richards simulation** Quantity: Matric head :math:h_m \, [\text{m}]. .. tip:: Typical use cases for Dirichlet conditions in a Richards simulation include: A Dirichlet boundary condition determines the value of the solution (here: matric head :math:h_m) at the boundary. Use cases in soil hydrology include: * Height above a fixed water table at the lower boundary. * Evaporative potential at upper boundary, if :math:h_m < z_\text{wt}, where :math:z_\text{wt} is the height above the water table. * Height above a fixed water table at lower boundary * Evaporative potential at upper boundary, if :math:h_m < z_\text{wt}, where :math:z_\text{wt} is the height above the water table. **Transport simulation** Quantity: Total concentration :math:C_t\,[\text{kg}\,\text{m}^{-d}] or concentration in the water phase :math:C_w\,[\text{kg}\,\text{m}^{-d}], depending on the value of concentration_type. The integer :math:d denotes the spatial dimension. Variables: * type: Dirichlet * value: Quantity as specified above. * concentration_type **(Transport only)**: Switch between total (:math:C_t) or water_phase (:math:C_w) concentration as defined above. * type: Dirichlet * value: Matric head :math:h_m in meters :math:\text{[m]} at the boundary. .. option:: Neumann .. object:: Neumann A Neumann boundary condition determines the value of target quantity flux at the boundary. A Neumann boundary condition determines the value of the solution gradient (here: water flux :math:\mathbf{j}_w) at the boundary. Use cases in soil hydrology include: **Richards Simulation** Quantity: Water flux :math:\mathbf{j}_w \, [\text{ms}^{-1}]. * Infiltration or evaporation of fixed fluxes at the upper boundary. Precipitation and evapotranspiration fluxes are typically measured with respect to a flat surface. For modeling these fluxes, the horizontal_projection key is used, which scales the flux applied to the boundary with its inclination with respect to the direction of gravitational force, Precipitation and evapotranspiration fluxes are typically measured with respect to a flat surface. For modeling these fluxes, the horizontal_projection key is used, which scales the flux applied to the boundary with its inclination with respect to the direction of gravitational force, .. math:: .. math:: j_{N, \text{scaled}} = \left| \mathbf{\hat{n}} \cdot \mathbf{\hat{g}} \right| j_N . .. note:: Hydraulic conductivity decreases with water content. Evaporation fluxes must not infinitely exceed the stable limit, or else the solver will inevitably fail. j_{N, \text{scaled}} = \left| \mathbf{\hat{n}} \cdot \mathbf{\hat{g}} \right| j_N . **Transport Simulation** Quantity: Solute flux :math:\mathbf{j}_s \, [\text{kg}\,\text{m}^{-d+1}\,\text{s}^{-1}], where :math:d indicates the spatial dimensions. Variables: * type: Neumann * value: Flux perpendicular to the surface :math:j_N, in the quantities defined above. Fluxes into the domain are negative, fluxes out of the domain positive. * horizontal_projection **(Richards only)**: Boolean if the actual boundary flux should be scaled with the surface inclination against the direction of gravity. * type: Neumann * value: Water flux in surface normal direction, :math:j_N, in volume per area per second :math:[\text{m]/\text{s}] at the boundary. Fluxes into the domain are negative, fluxes out of the domain positive. * horizontal_projection: Boolean if the actual boundary flux should be scaled with the surface inclination. .. option:: Outflow (Transport only) .. note:: Hydraulic conductivity decreases with water content. Evaporation fluxes must not infinitely exceed the stable limit, or else the solver will inevitably fail. An outflow boundary condition allows solute be transported throw the boundary by the water flux. As solute concentration and water flux are only modelled inside the domain, this effectively only allows the solute to leave the domain and be discarded. The boundary condition value is an additional solute flux for which all considerations of a Neumann boundary condition apply (see above). Quantity: Solute flux :math:\mathbf{j}_s \, [\text{kg}\,\text{m}^{-d+1}\,\text{s}^{-1}], where :math:d indicates the spatial dimensions. The total solute flux through the boundary is then given by .. math:: j_s = \left| \mathbf{j}_s \cdot \mathbf{\hat{n}} \right| + j_N , where :math:\mathbf{j}_s = C_w \mathbf{j}_w is the solute flux at the boundary, :math:\mathbf{\hat{n}} is the boundary unit normal vector and :math:j_N is the given boundary condition value, as defined below. Variables: * type: Outflow * value: Flux perpendicular to the surface :math:j_N, as in :option:Neumann. This flux is applied in addition to regular seepage through the boundary. It is recommended to set this value to 0 (zero). .. _YAML: https://gettaurus.org/docs/YAMLTutorial/
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