24th September 2015

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.

- 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.

1 Two-dimensional Channel flow (optional)

1.1 Mesh generation

1.2 Computation of the base flow

1.3 Stability analysis

2 Backward-facing step

2.1 Computation of the base flow

2.2 Stability analysis

3 Flow past a cylinder

3.1 Computation of the base flow

3.2 Stability analysis

4 Three-dimensional Channel flow

5 Solutions

1.1 Mesh generation

1.2 Computation of the base flow

1.3 Stability analysis

2 Backward-facing step

2.1 Computation of the base flow

2.2 Stability analysis

3 Flow past a cylinder

3.1 Computation of the base flow

3.2 Stability analysis

4 Three-dimensional Channel flow

5 Solutions

[next]