Global Instability Computations with Nektar++

The aim of this tutorial is to introduce the user to the spectral/hp element framework Nektar++ and its use for global stability computations. Information on how to install the libraries, solvers, and utilities on your own computer is available on the webpage www.nektar.info.

Task 0.1 Prepare for the tutorial. Make sure that you have:

Compiled, installed and tested Nektar++ .
By default it will install all executables in the sub-directory dist/bin of the build directory you created:
e.g. MyHomeDirectory/nektar++/build/dist/bin.
We will refer to this directory as $NEK for the remainder of the tutorial.
Downloaded the tutorial files from
http://www.nektar.info/docs/tutorial/stability-_tutorial.tar.gz
Unpack it using tar -xvf stability-tutorial.tar.gz to produce directories called TutorialFiles and TutorialFilesComplete each containing the subdirectories
- BackwardStep
- Channel
- Channel-3D
- Cylinder
We will refer to the TutorialFiles directory as $NEKTUTORIAL.

Additionally, you should also install

a visualization package capable of reading VTK files, such as ParaView (which can be downloaded from here) or VisIt (downloaded from here). Alternatively, you can generate Tecplot formatted .dat files for use with Tecplot.
a plotting program capable of reading data from ASCII text files, such as GNUPlot or MATLAB.

Optionally, you can install the open-source mesh generator Gmsh (which can be downloaded from here) to generate the meshes for the tutorial examples yourself. However, pre-generated meshes are provided.

In the first section we will cover the stability analysis of a two-dimensional channel flow, through both a splitting scheme (the Velocity Correction Scheme) and the direct inversion algorithm (also referred to as the Coupled Linearised Navier-Stokes solver). We will then study the transient growth of the flow past a backward-facing step in section 2 and the direct/adjoint stability analysis of a flow past a cylinder in section 3. Finally, in section 4, we will briefly show the application of the stability tools presented to a three-dimensional channel flow test case.