In this section, we detail how to use the steady-state solver (that implements the selective frequency damping method, see Sec. 11.1.5). Two cases are detailed here: the execution of the classical SFD method and the adaptive SFD method, where the control coefficient χ and the filter width Δ of the SFD method are updated all along the solver execution. For the second case, the parameters of the SFD method do not need to be defined by the user (they will be automatically calculated all along the solver execution) but several session files must be defined in a very specific way.
The definition of
Projection is similar as what
is explained in 11.4.1. The use of the steady-state solver is enforced through the
definition of the
Driver which has to be
not need to be defined to run the unadapted SFD method (by default, it is set to
The following parameters can be specified in the
PARAMETERS section of the session
Kinvis: sets the kinematic viscosity ν. It is typically 1∕Re if both the characteristic velocity and characteristic length are chosen to be 1.
ControlCoeff: sets the control coefficient χ of the SFD method. Default value: 1.
FilterWidth: sets the filter width Δ of the SFD method. Default value: 2.
FrequencyEV: if the growth rate and the frequency of the dominant eigenvalue are known, they can be given given as input and the code will automatically select the optimum parameters χ and Δ (and overwrite the values of
GrowthRateEVthat may be given in the session file)
TOL: sets the tolerance of the SFD method. The code will run until ||q -q||inf < TOL. Default value: 10-8.
Note that for the steady-state solver, the parameter
NumSteps is not taken into account. The
solver will run until a steady-state solution is found and not for a pre-defined number of time
Running the adaptive selective frequency damping method requires to set up the
session files in a very specific manner. First, the
Geometry section must be in a
separated archive file. If the test case studied is called "Session", the mesh file must
Session.xml.gz (the linux command "gzip" can be used to obtain this
The requirements for the file
Session.xml are similar as for the ones for the classical
SFD method. The
Geometry section being removed and placed in
This file defines the properties of the nonlinear problem solved (i.e. the flow for
which we want a steady-state). Also, the
SOLVERINFO section must contain the line:
The adaptive SFD method used is coupled with a stability analysis method. Then
nits should be defined into the
PARAMETERS section of
Session.xml. If not, these
parameters will take the default values presented in Sec. 11.4.
The goal of running the stability analysis is to evaluate the dominant eigenvalue of a “partially converged” steady base flow. This approximation is then used by the steady-state solver to select a control coefficient χ and a filter width Δ then ensure a fast convergence towards a steady-state solution.
To define the linear stability problem, another file, that must be called
has to be defined. This file must be an exact copy/paste of
Session.xml, only three
things have to be modified:
InitialConditionshas to be defined.
BaseFlowhas to be defined (it will be overwritten all along the solver execution). We recommend it to be a copy of
Once these three files (the
Session.xml.gz, the nonlinear problem definition in
Session.xml and the homogeneous linear problem in
Session_LinNS.xml) are correctly
defined, the adaptive SFD method must be executed using: