Pressure Stabilization Scaling

Pressure Stabilization Scaling = <float>

Description / Usage

This optional card is only used if the Pressure Stabilization card is set to yes, where

<float>

tau, a positive real value ( tau > 0.0 ) that scales the momentum residual being added to the continuity equation for pressure stabilization.

The default value of tau is 0.1. If the Pressure Stabilization card is omitted, or set to no, then tau is ignored.

Examples

Following is a sample card:

Pressure Stabilization Scaling = 0.01

Technical Discussion

Generally, if tau is small, then more accurate solutions may be obtained at the cost of a more ill-conditioned matrix system that may not be easily amenable to iterative solvers (but stay tuned!). Conversely, larger values of this parameter result in equation systems that are easier to solve using the available iterative matrix solvers, but the solution thus obtained may be less accurate. A good choice for tau is 0.1.

The scaling value, tau, is further scaled inside of Goma. Knowledge of this scaling is sometimes useful. First, an average Reynolds number (Re) is computed according to:

\[\mathrm{Re} = \frac{\rho \lVert U \rVert \langle h \rangle }{2 \mu}\]

where \(\rho\) and \(\mu\) are local values for density and viscosity, \(\lVert U \rVert\) is a norm of the velocity field, and \(\langle h \rangle\) is a global average value for element size. If Re < 3.0, the pressure stabilization scaling is given by this expression:

\[\frac{ \mathrm{tau} {\langle h \rangle}^2 }{12 \mu}\]

On the other hand, if Re > 3.0, the following scales the pressure stabilization terms in the continuity equation:

\[\frac{ \mathrm{tau} {\langle h \rangle} }{2 \rho \lVert U \rVert}\]