The Brinkman Equations (br) interface (), found under the Porous Media and Subsurface Flow branch () when adding a physics interface, is used to compute fluid velocity and pressure fields of single-phase flow in porous media in the laminar flow regime. The physics interface extends Darcy’s law to describe the dissipation of the kinetic energy by viscous shear, similar to the Navier–Stokes equations. Fluids with varying density can be included at Mach numbers below 0.3. Also the viscosity of a fluid can vary, for example, to describe non-Newtonian fluids. To simplify the equations, select the Stokes–Brinkman flow feature to reduce the dependence on inertial effects when the Reynolds number is significantly less than 1. The physics interface can be used for stationary and time-dependent analyses.

When this physics interface is added, the following default nodes are also added in the Model Builder — Porous Medium, Wall (the default boundary type, using No slip as the default boundary condition), and Initial Values. Then, from the Physics toolbar, add other nodes that implement, for example, boundary conditions and volume forces. You can also right-click Brinkman Equations to select physics features from the context menu.

In the COMSOL Multiphysics Reference Manual see Table 2-4 for links to common sections such as Discretization, Consistent Stabilization, Inconsistent Stabilization, and Advanced Settings, all accessed by clicking the Show button () and choosing the applicable option. You can also search for information: press F1 to open the Help window or Ctrl+F1 to open the Documentation window.

The Label is the default physics interface name.

The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.

The default Name (for the first physics interface in the model) is br.

By default the physics interface uses the Incompressible flow formulation of the Brinkman equations to model constant density flow. Alternatively, from the Compressibility list select Weakly compressible flow, which should be used when the pressure dependency of the density can be neglected, or Compressible flow (Ma<0.3) to solve for the full compressible flow of which, however, the Mach number must be below 0.3.

For 2D axisymmetric models, select the Swirl flow check box to include the swirl velocity component, that is the velocity component in the azimuthal direction. While can be nonzero, there can be no gradients in the direction.

Note that this feature is only available for specific modules. See https://www.comsol.com/products/specifications/ for a detailed overview.

The Neglect inertial term (Stokes–Brinkman) check box is selected by default to model flow at low Reynolds numbers for which the inertial term can be neglected. This results in the linear Stokes–Brinkman equations.

Gravity is not included by default. Select the Include gravity check box to activate the acceleration of gravity. This automatically adds a global Gravity feature node to the interface model tree, and the buoyancy force is included in the Equations.

Also, when the Include gravity check box is selected, the Use reduced pressure option changes the pressure formulation from using the total pressure (default) to using the reduced pressure. This option is suitable for configurations where the density changes are very small; otherwise, the default formulation can be used. For more information, see Gravity.

Choose how the No Slip condition on Wall boundaries and Interior Wall boundaries adjacent to Porous Medium should be treated. The options are Standard no slip formulation (default) and Porous slip. The latter option provides a unified treatment when the porous matrix is fully resolved as well as when it is under-resolved ensuring a smooth transition between regions with different resolutions; see No Slip under Wall in the The Creeping Flow, Laminar Flow, Turbulent Flow, Large Eddy Simulation, and Detached Eddy Simulation Interfaces section.

Enter a Reference pressure level pref (SI unit: Pa). The default value is 1[atm].

Enter a Reference temperature level Tref (SI unit: K). The default value is 293.15[K].

If Include gravity is selected, a Reference position rref (SI unit: m) can be specified which is then used for the calculation of the hydrostatic pressure.

Turbulent flow can be simulated by changing the Turbulence model type to RANS (Reynolds-Averaged Navier–Stokes). If turbulent flow is activated, you can set the Turbulence model either to one of the algebraic turbulence models, Algebraic yPlus (the default) or L-VEL, or to one of the following two-equation turbulence models: k-ε, Realizable k-ε, Low Reynolds Number k-ε, k-ω, SST and v2-f. The Wall treatment is set to Automatic (default) or Low Re while Wall functions is available for k-ω and is the only option for k-ε and Realizable k-ε. For more information about turbulence modeling, see Theory for the Turbulent Flow Interfaces in the CFD Module User’s Guide.

The following dependent variables (fields) are defined for this physics interface — the Velocity field u (SI unit: m/s) and its components, and the Pressure p (SI unit: Pa).

To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box. Normally these settings do not need to be changed.

The Use pseudo time stepping for stationary equation form option adds pseudo time derivatives to the equation when the Stationary equation form is used in order to speed up convergence. When selected, a CFL number expression should also be defined. For the default Automatic option, the local CFL number (from the Courant–Friedrichs–Lewy condition) is determined by a PID regulator.