functionDiscretization
Extends from TransiEnt.Basics.Icons.Function.
Information
1. Purpose of model
Pure function that transforms user-defined grid section specifications into the complete set of geometric arrays required by the ATES control volume models. Computes radii, heights, surface areas, cross-sectional areas, and volumes for both the aquifer and the overlying and underlying confining (aquitard) layers.
2. Level of detail, physical effects considered, and physical insight
(Purely technical component without physical modeling.)
3. Limits of validity
- Assumes cylindrical geometry (radial symmetry).
- Confining layer grid is mirrored: upper layer uses the specified section heights, lower layer uses them in reverse order.
4. Interfaces
Inputs:
R_GS_H[:] — number of control volumes in each radial grid section [-]
dx_GS[:] — radial thickness of control volumes per section [m]
r_0 — well screen radius [m]
H_GS_VA[:] — number of control volumes in each vertical aquifer section [-]
dz_GS_A[:] — height of aquifer control volumes per section [m]
H_GS_VC[:] — number of control volumes in each vertical aquitard section [-]
dz_GS_C[:] — height of aquitard control volumes per section [m]
Outputs:
r[N_r] — outer edge radius of radial control volumes [m]
r_r[N_r, N_z] — centre radius of aquifer control volumes [m]
r_r_c[N_r, N_z_c] — centre radius of aquitard control volumes [m]
z_A[N_r, N_z] — height of aquifer control volumes [m]
z_Cu[N_r, N_z_c] — height of upper aquitard control volumes [m]
z_Cd[N_r, N_z_c] — height of lower aquitard control volumes [m]
A_s[N_r, N_z] — outer lateral surface area of aquifer control volumes [m²]
A_q[N_r] — cross-sectional (annular) area of control volumes [m²]
V[N_r, N_z] — volume of aquifer control volumes [m³]
5. Nomenclature
 |
r |
outer edge radius of control volume [m] |
 |
z_A |
height of aquifer control volume [m] |
 |
A_s |
outer lateral surface area [m²] |
 |
A_q |
cross-sectional annular area [m²] |
 |
V |
control volume [m³] |
 |
N_r = sum(R_GS_H) |
total number of radial control volumes [-] |
 |
N_z = sum(H_GS_VA) |
total number of vertical aquifer control volumes [-] |
 |
r_0 |
well screen radius [m] |
6. Governing Equations
(no equations)
7. Remarks for Usage
Called once during initialization via the Geometry model. Not intended for direct instantiation in simulation models.
8. Validation
Tested in check model "ATES.Check.TestDiscretization"
9. References
(no remarks)
10. Version History
Model created by Markus Gillner (markus.gillner@tuhh.de), May 2026
Inputs
| Type | Name | Default | Description |
|---|---|---|---|
| Integer[:] | R_GS_H | Length of horizontal grid sections | |
| SI.Length[:] | dx_GS | Thicknes of the control volumes within the grid sections | |
| SI.Length | r_0 | Radius of pipe in well | |
| Integer[:] | H_GS_VA | Heigth of vertical grid sections within the aquifer | |
| SI.Length[:] | dz_GS_A | Heigth of the control volumes within the grid sections of the aquifer | |
| Integer[:] | H_GS_VC | Heigth of vertical grid sections within the aquitard | |
| SI.Length[:] | dz_GS_C | Heigth of the control volumes within the grid sections of the aquitard |
Outputs
| Type | Name | Default | Description |
|---|---|---|---|
| SI.Length[sum(R_GS_H)] | r | radius to the outer edge of control volumes | |
| SI.Length[sum(R_GS_H),sum(H_GS_VA)] | r_r | radius to the center of the control volumes in aquifer | |
| SI.Length[sum(R_GS_H),sum(H_GS_VC)] | r_r_c | radius to the center of the control volumes in confined layers | |
| SI.Length[sum(R_GS_H),sum(H_GS_VA)] | z_A | height of control volumes in aquifer | |
| SI.Length[sum(R_GS_H),sum(H_GS_VC)] | z_Cu | height of control volumes in upper confined layer | |
| SI.Length[sum(R_GS_H),sum(H_GS_VC)] | z_Cd | height of control volumes in lower confined layer | |
| SI.Area[sum(R_GS_H),sum(H_GS_VA)] | A_s | outer surface area of control volumes of aquifer | |
| SI.Area[sum(R_GS_H)] | A_q | cross-sectional area of control volumes of aquifer and confined layer | |
| SI.Volume[sum(R_GS_H),sum(H_GS_VA)] | V | volume of control volumes of aquifer | |
| SI.Area[sum(R_GS_H),sum(H_GS_VC)] | A_s_Cu | outer surface area of control volumes of upper confined layer | |
| SI.Volume[sum(R_GS_H),sum(H_GS_VC)] | V_Cu | volume of control volumes of upper confined layer | |
| SI.Area[sum(R_GS_H),sum(H_GS_VC)] | A_s_Cd | outer surface area of control volumes of lower confined layer | |
| SI.Volume[sum(R_GS_H),sum(H_GS_VC)] | V_Cd | volume of control volumes of lower confined layer |