Chapter 1

This tutorial describes the use of the spectral/hp element framework Nektar++ to explore one of the classical and canonical problems of fluid dynamics: the Taylor-Green Vortex (TGV). Information on how to install the libraries, solvers, and utilities on your own computer is available on the webpage

Task: 1.1 Prepare for the tutorial. Make sure that you have:

The TGV flow case has analytical initial conditions and its exact solution is known from direct numerical simulation (DNS) using incompressible Navier-Stokes solvers. For this reason it is often used for code validation. Moreover, the TGV flow problem is a very instructive analysis case: through its numerical simulation, it is possible to study turbulent transition and decay, vortex dynamics and energy dissipation mechanisms 1. In this tutorial we will focus on the solution of the TGV flow case in a 3D cube region within a time frame of 20 seconds, which is usually sufficient to observe the aforementioned phenomena. For now, we will restrict ourselves to a resolution of 643 degrees of freedom using p = 8 order interpolants in a Continuous Galerkin (CG) projection. We will also have a look at the temporal evolution of the kinetic enery and its dissipation rate in the flow domain. The case with 1283 degrees of freedom is left as an optional exercise for the user.

The necessary files to complete this tutorial are included in the .zip folder downloaded using the link in Task 1.1. Under the folder tutorial, the user will find four subfolders, two for each resolution (64 or 128):

The folder completed that can also be found in the .zip contains the filled .xml files to be used as a check in case the user gets stuck, or to verify the correctness at the end of the tutorial.


Because the test case can take some time to complete, you may want to run the solver with the completed configurations files available in the folder completed. To do so, in the folder completed/solver64, type the following command on the command line:

$NEK/IncNavierStokesSolver TGV64_mesh.xml TGV64_conditions.xml

Note that this is entirely optional as output files are already provided in the same folder, i.e. completed/solver64.