The Brinkman Equations Interface
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.
The main node is the Fluid and Matrix Properties feature, which adds the Brinkman equations and provides an interface for defining the fluid material and the porous matrix.
When this physics interface is added, the following default nodes are also added in the Model BuilderFluid and Matrix Properties, 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.
The boundary conditions are essentially the same as for the Laminar Flow interface. Differences exist for the following boundary types: Outlet, Symmetry, Open Boundary, and Boundary Stress where the viscous part of the stress is divided by the porosity to appear as
In the COMSOL Multiphysics Reference Manual see Table 2-4 for links to common sections such as Discretization, Consistent Stabilization, and Inconsistent Stabilization, and Advanced Settings sections, 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.
Physical Model
This node specifies the properties of the Brinkman Equations interface, which describe the overall type of fluid flow model.
By default the physics interface uses the Incompressible flow formulation of the Brinkman equations to model constant density flow. Alternatively, select Compressible flow (Ma<0.3) from the Compressibility list if there are small variations in the density, typically dependent on the temperature (nonisothermal flow). For compressible flow modeled with the Brinkman Equations interface, the Mach number must be below 0.3.
Neglect Inertial Term (Stokes–Brinkman Flow)
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.
Enable porous media domains
The Enable porous media domains check box is selected by default to solve Brinkman equations in porous domains.
Reference Pressure Level
Enter a Reference pressure level pref (SI unit: Pa). The default value is 1[atm].
Swirl Flow
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.
Dependent Variables
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).
Advanced Settings
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.
Pseudo Time Stepping for Laminar Flow Models and Pseudo Time Stepping in the COMSOL Multiphysics Reference Manual