The momentum equation (Equation 3-15 or
Equation 3-17) 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.
The time-scale tensor 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 does not, 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. The COMSOL Multiphysics software 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 time scale is activated.
The Limit small time steps effect on stabilization time scale option can be used to ramp down the time-step contribution in the stabilization when the time step becomes much smaller than the convective and diffusive time scales. This option prevents loss of pressure stabilization at such small time steps.