# Third Year Project

This page contains the informations for the third year students working under the supervision of Dr Revell working on their research project.

### Taylor Green Vortices

Taylor Green vortices is a classical numerical test case in order to check the energy conservation of a code. The initial solution has the following form %BEGINLATEX% $$\left\{ \begin{array}{c} u_{1}=-\sin(kx_{1})\cdot\cos(kx_{2})\u_{2}=\cos(kx_{1})\cdot\sin(kx_{2})\end{array}\right.\label{eq: T-G vel field}$$ %ENDLATEX% and the pressure is expressed by: %BEGINLATEX% $$p=-\frac{1}{4}\left[\cos(2kx_{1})+\cos(2kx_{2})\right]\label{eq: p field T-G}$$ %ENDLATEX% where %$k=1,2,...$% is an arbitrary constant. The number of vortices in each direction is equal to %$2\times k$%. In this analysis the constant is set equal to 1.

Steps to do to run the simulation:

1. Set the calculation as transient
2. Laminar case (no turbulence model)
3. inviscid case (viscosity %$\mu = 0$%)
4. periodic boundary conditions:
• periodic on the 4 edges of the square %$x = 0 \, \& \, x= 2 \pi$% and %$y = 0 \, \& \, y= 2 \pi$%
• symmetry on the front and rear
5. Set a time step for which the CFL max is well below 1 (an example could be %$\delta t = 1e-3$%
6. Set the convective scheme to a full central difference (CD).
7. Set the residual for a variable resolution to 1e-8 (this is not the convergence criteria, it is the residual for the resolution of the linear system).
8. Run the simulation for 30000 time steps.
9. At the end of every time step compute the total kinetic enery as %$K=0.5(u_{1}^2+u_{2}^2)$%

The conformal 60x60 mesh for the case can be download from here.

• Code_Saturne: refer to this page to have the fortran to run the case
• STAR-CD: here you can download the setup for the case for version 4.02. The archive cointain:
• .MAC: macro that set up the case, from meshing generation to boundary conditions, to all numerical parameters
• ufile: folder with the user fortran (NB in order to use the fortran the installation of Absoft fortran could be required, have a try and let me know if you have problem)
• posdat: subroutine for the post processing (call at the end of every time step, the analogue of usproj under saturne)
• initfi: subroutine to inizialize the field
• FLUENT: try to follow the same step, if you have any problem to set up the case let me know

• New meshes with different resolution:

• : Star-CD macro to generate the unv mesh

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Topic attachments
I Attachment Action Size Date Who Comment
msh Taylor_120x120.msh manage 3720.9 K 2009-11-30 - 10:48 UnknownUser Mesh TG vor 120x120 Fluent
unv Taylor_120x120.unv manage 8259.2 K 2009-11-30 - 10:48 UnknownUser Mesh TG vor 120x120 Ideas
msh Taylor_40x40.msh manage 390.6 K 2009-11-30 - 10:47 UnknownUser Mesh TG vor 40x40 Fluent
unv Taylor_40x40.unv manage 940.7 K 2009-11-30 - 10:47 UnknownUser Mesh TG vor 40x40 Ideas
zip Taylor_star.zip manage 137.0 K 2009-10-15 - 12:57 UnknownUser T&G vortices STAR-CD V4.02
MAC grid_taylor_SAT.MAC manage 3.4 K 2009-12-01 - 18:24 UnknownUser StarCD macro to generate the unc mesh
unv tay60_conf.unv manage 2090.7 K 2009-10-15 - 12:39 UnknownUser T&G vortices mesh conformal
Topic revision: r5 - 2009-12-01 - 18:25:10 - StefanoRolfo
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24 Aug 2019

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