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 button (
) and select
Stabilization.
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. 7) and were later extended to Galerkin least-squares (GLS) applied to the Navier-Stokes equations (
Ref. 8). This is the streamline diffusion formulation that COMSOL Multiphysics
supports. The time-scale tensor is the diagonal tensor presented in
Ref. 9.