modelDarcyFlow_vertical

Information

1. Purpose of model

Implements the vertical Darcy momentum equation including the buoyancy body force. Computes vertical mass flow rates and Darcy velocities at all N_z+1 horizontal interfaces of the aquifer grid. When buoyancy is disabled, vertical flow is set to zero.

2. Level of detail, physical effects considered, and physical insight

L4: Resolved vertical flow field for each horizontal cell interface across the full [N_r, N_z+1] grid. Buoyancy is driven by local density differences and can be switched on/off via the Boolean parameter with_buoyancy. Inertial terms are neglected.

3. Limits of validity

- Valid for low Reynolds number flow (Darcy regime).

- With buoyancy disabled, vertical flow is identically zero (no short-circuit between layers).

4. Interfaces

No connectable ports. Variables are accessed via Modelica inner/outer mechanism from the enclosing ControlVolumeL4:

delta_p_v[N_r, N_z+1] — vertical pressure differences (outer, set by ControlVolumeL4)

rho_FM_v[N_r, N_z+1] — fluid density at horizontal interfaces (outer)

f_eta_v[N_r, N_z+2] — dynamic viscosity at interfaces (outer)

5. Nomenclature

	m_flow_buoyancy[N_r, N_z+1]	vertical mass flow rate at each interface [kg/s]
	v_darcy[N_r, N_z+1]	vertical Darcy velocity at each interface [m/s]
	delta_p_v	vertical pressure difference [Pa]
	k	vertical permeability [m²]
	f_eta_v	dynamic viscosity [Pa·s]
	rho_FM_v	fluid density at interface [kg/m³]
	g_n	gravitational acceleration = 9.81 m/s²
	z_diff[N_z+1]	distance between temperature nodes of adjacent control volumes [m]
	A_q[N_r]	cross-sectional area of control volume [m²]

6. Governing Equations

Vertical Darcy momentum equation with gravitational body force:

Buoyancy mass flow rate from Darcy velocity and cross-sectional area:

7. Remarks for Usage

This model must be instantiated inside ControlVolumeL4 so that the inner/outer variable declarations are satisfied. It cannot be used as a standalone component. The buoyancy switch is propagated from the Setting record.

8. Validation

Tested in check model "ATES.Validierung.Buoyancy.Val_homogenLayer"

9. References

(no remarks)

10. Version History

Model created by Markus Gillner (markus.gillner@tuhh.de), May 2026

Parameters

Components