Performs stability analsysis for incompressible flows by solving the Orr-Sommerfeld equation for planar channel flow, the Blasius boundary layer, or for a given arbitary mean velocity profile. Note that in all cases, the parallel-flow approximation is made.
Several different solvers are provided using different numerical methods including stablized shooting, Chebyschev spectral collocation, and finite-difference discretization. Solvers are also provided for both temporal analysis (real wavenumber, complex wave speed) and the more realistic spatial analysis (real frequency, complex wavenumber).
Also includes bl.f which is a spectral collocation Blasius flow solver and there are
also shooting-based Blasius solvers embedded within the stability solvers (see below).
As an example, the mean Blasius velocity profile and second derivative of that profile computed
using contebl.f is shown below.
The eigenfunction for the most unstable Tollmien-Schlichting wave (TS-wave) at Re=5800,
alpha=0.179 is shown in the following figure with an complex valued wave speed
(eigenvalue) of c = 0.36412287E+00 + i 0.79597206E-02.
These results are from running contebl.f using default input parameters as
described below.
Note that there are example scripts for making plots of results using
gnuplot. These scripts have files *.com such as mean.com for
plotting the mean flow profile and phi.com for plotting the eigenfunction,
phi.
There are also example scripts for plotting these same results using Python
and matplotlib. See mean.py and phi.py and these are used by typing
python mean.py
which generates the file mean.png. Similarly for phi.py.
Should build on Linux and MacOS platforms with Gfortran. First, as usual, you will clone the repository from GitHub using a command such as:
git clone https://github.com/sscollis/os-stab.git
You can get simple help on building the applications(s) by typing:
make help
And the default build is simply:
make
Recommended build is:
make USE_RKCK45=1
You can make the Doxygen documentation using:
make docs
and then you can view the documentation locally by pointing your browser at
html/index.html. For example, on a Mac you type
open html/index.html
from within the main os-stab directory to view the Doxygen documentation.
The simplest case is temporal stability analysis for a planar channel using Conte's method and shooting:
./conte
Enter "d" for default values
A similar analysis for the Blasius boundary layer is done using:
./contebl
Enter "d" for default values
or the similar which takes input fron stdin
./orrsom < test.inp
Just computing the Blasisus boundary layer alone (no eigenanalysis):
./bl < bl.inp
A spatial analysis for BL is done using:
./orrspace
And then type space.inp for input file.
You can do a sweep through the stability curve using:
./orrspace
And enter sweep.inp as the input file.
These examples require that one currently builds with USE_ALL_NR=1 that
requires the user to supply commercially licenses code from Numerical Recipes
in a file called nr.f. These routines are currently only used sparingly and
can/should be replaced with open source code as time permits.
Nevertheless, you must have a valid license to use Numerical Recipes code and you must now check such code into this repository!
To do a sweep in alpha using finite-differences:
orrfdchan < fd-128.inp
or a single alpha and printing the eigenfunction:
orrfdchan < fdchan.inp
NOTE: There currently are not example inputs for all codes!
Updated Orr-Sommerfeld solvers for gfortran
| Code | Description |
|---|---|
conte.f |
Solves OS for channel using Godunov-Conte shooting |
contebl.f |
Solve Blasius and then OS for boundary layer using Conte |
bl.f |
Spectral collocation solver for Blasius equation |
orrsom.f |
Similar to contebl.f |
shoot.f |
Collection of general routines for shooting |
orrspace.f |
Solves spatial problem for boundary layers can sweep in frequency |
orrfdchan.f |
Solves temporal channel problem using finite-differences including sweeps |
Numerous updates in this version include:
- Fixed bug in eigenfunction values at nstep
- Improved orthonormalization criteria
- Switch from IMSL to LAPACK (need to test still)
- Updated to support gfortran in makefile
- Added scripts for gnuplot output
- Improved some inline documentation
- Use OpenBLAS for numerical linear algebra
- Works on Mac OS-X (Darwin)
Incompressible Orr--Sommerfeld Solvers for Channel flow and Blasius Boundary
Layer. Also bl.f is a spectral blasius flow solver.
I have updated the following codes to use LAPack routines
orrncbl.f This finds the neutral curve for Boundary layer and
channel profiles
orrcolchan.f Solve Orr-Sommerfeld for channel profile
S. Scott Collis
flow.physics.simulation@gmail.com