The momentum equation (Equation 13-7 or
Equation 13-9) is a (nonlinear) convection-diffusion equation. Such equations can easily become unstable if discretized using the Galerkin finite element method. Stabilized finite element methods are usually necessary in order to obtain physical solutions. The stabilization settings are found in the main Fluid Flow interface features. To display this section, click the
Show More Options button (
) and select
Stabilization in the
Show More Options dialog box.
There are three types of stabilization methods available for Navier-Stokes — streamline diffusion,
crosswind diffusion, and
isotropic diffusion. Streamline diffusion and crosswind diffusion are consistent stabilization methods, whereas isotropic diffusion is an inconsistent stabilization method.
For strongly coupled systems of equations, the streamline diffusion method must be applied to the system as a whole rather than to each equation separately. These ideas were first explored by Hughes and Mallet (Ref. 8) and were later extended to Galerkin least-squares (GLS) applied to the Navier-Stokes equations (
Ref. 9). This is the streamline diffusion formulation that COMSOL Multiphysics
supports. The time-scale tensor is the diagonal tensor presented in
Ref. 10.
The time-scale tensors for time-dependent problems should in theory depend on a time-scale that many references just set to the time-step taken by the time-solver, Δt (see for example
Ref. 9 and
Ref. 10). This simple approach doesn’t however necessarily reflect on the actual time-scales in the physics. A typical example is reacting flows where the time-step is often guided by fast reactions, while the flow develops relatively slowly. COMSOL Multiphysics can therefore replace
Δt2 in the time scale tensor with measures of type
which are calculated from projections of weak expressions in a fashion similar to those in
Ref. 11. These measures of the time scale are used when
Use dynamic subgrid timescale check box is selected. Streamline diffusion is active by default because it is necessary when convection is dominating the flow.