Linear Stability#

Linear Stability = {char_list}

Description / Usage#

This optional card indicates whether or not linear stability analysis should be performed, as well as what kind.

The valid options for {char_list} are:

no

Do not perform any kind of linear stability analysis.

yes

Perform regular linear stability analysis. If your problem was 2D, then 2D analysis is performed. If your problem was 3D, then 3D analysis is performed.

inline

Same as yes, perform regular linear stability analysis.

3D

Subject the 2D flow to 3D linear stability analysis by normal mode expansion for the modes specified with the Eigen Wave Numbers card.

file

Set up the problem as in yes or inline, but output the matrices involved instead of determining stability.

3Dfile

Set up the problem as in 3D, but output the matrices involved instead of determining stability.

The default value is no.

Examples#

Here is a sample card:

Linear Stability = yes

Technical Discussion#

When linear stability analysis is performed, a steady-state solution is first acquired, and then the eigenvalue/eigenvector spectrum is computed subject to the choices made in the Eigensolver Specifications section. In the case of file or 3Dfile, the steady-state solution is acquired and then the matrices that would have been used to compute the spectrum are exported to file and no spectrum is actually computed. Refer to the Advanced Capabilities (Gates, et. al., 2001) document for a more thorough description.

The name of the output files when file is specified are:

  • LSA_mass_coo.out for the mass matrix, B or M,

  • LSA_jac_coo.out for the jacobian matrix, J,

  • LSA_vars.out for variable names associated with unknowns.

When 3Dfile is specified, the names are:

  • LSA_mass_coo-<f>.out, for the mass matrix, B or M,

  • LSA_jac_coo-<f>.out, for the jacobian matrix, J,

  • LSA_vars.out, for variable names associated with unknowns.

where <f> is the value of the requested normal mode (see the Eigen Wave Numbers card). The Eigen Matrix Output card must be set to yes in order to create and write these files.

When computing the 3D stability of a base 2D flow, other modifications need to be made (see the 3D stability of 2D flow memo).

See the Advanced Capabilities document (Gates, et. al., 2001), or it’s replacement (Labreche, et. al., 2002).

References#

SAND2000-2465: Advanced Capabilities in Goma 3.0 - Augmenting Conditions, Automatic Continuation, and Linear Stability Analysis, I. D. Gates, D. A. Labreche and M. M. Hopkins (January 2001)

SAND2002-xxxx: Advanced Capabilities in Goma 4.0 - Augmenting Conditions, Automatic Continuation, and Linear Stability Analysis, Labreche, D. A., Wilkes, E. D., Hopkins, M. M. and Sun, A. C., (in preparation)