Global Instability Computations with Nektar++ 


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

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

Additionally, you should also install

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