Stabilization#

To solve the Navier-Stokes equations (and other), Lethe uses stabilization techniques to formulate a Petrov-Galerkin strategy in which the test function is not strictly equal to the interpolation. The stabilization provided by Lethe are relatively robust and do not require any manual tinkering. However, stabilization of FEM schemes remain an active area a research, notably when it comes to variational multi-scales (VMS) methods. This is a field in which we are doing active research. As such, Lethe possesses some advanced parameters to control the stabilization techniques used to solve the Navier-Stokes. These are advanced parameters and, in general, the defaults value should be used.

subsection stabilization
  set use default stabilization        = true

  set stabilization                    = pspg_supg     # <pspg_supg|gls|grad_div>.

  # DCDD stabilization
  set heat transfer dcdd stabilization = false
  set vof dcdd stabilization           = true

  # Pressure scaling factor
  set pressure scaling factor          = 1
end

The use default stabilization indicates that the solver should use the default stabilization strategy, which is generally the most adequate strategy. To use an alternative strategy, this parameter must be set to false and the strategy to be used must be manually specified using the stabilization parameter.

There are three choices of stabilization strategy:

  • stabilization=pspg-supg assembles a PSPG/SUPG stabilization for the Navier-Stokes equations. This stabilization should only be used with the monolithic solver for the Navier-Stokes equations (lethe-fluid or lethe-fluid-matrix-free).

  • stabilization=gls assembles a full GLS stabilization for the Navier-Stokes equations which adds two Least-Squares terms (for more details see On the Need for Stabilization). This stabilization should only be used with the monolithic solver for the Navier-Stokes equations (lethe-fluid or lethe-fluid-matrix-free).

  • stabilization=grad_div assembles a grad-div penalization term in the momentum equation to ensure mass conservation. This is not a stabilization method per-say and should not be used with elements that are not LBB stable. This stabilization should only be used with the grad-div block Navier-Stokes solver (lethe-fluid-block).

  • heat transfer dcdd stabilization: Applies the dDiscontinuity-Capturing Directional Dissipation (DCDD) stabilization term on the heat transfer equation. For more information, see Tezduyar, T. E. (2003).

  • vof dcdd stabilization: Applies the DCDD stabilization term on the VOF equation. For more information, see Tezduyar, T. E. (2003).

The pressure scaling factor parameter is used as a multiplier for the pressure in the momentum equation; the inverse of the factor is applied to the pressure after solving. It helps the convergence of the linear solver by decreasing the condition number for cases where pressure and velocity have very different scales.