# Turbulence statistics in a spectral element code: a toolbox for High-Fidelity Simulations

## Abstract

In the present document we describe a toolbox for the spectral-element code Nek5000, aimed at computing turbulence statistics. The toolbox is presented for a small test case, namely a square duct with L _{x} = 2h, L _{y} = 2h and L _{z} = 4h, where x, y and z are the horizontal, vertical and streamwise directions, respectively. The number of elements in the xy-plane is 16 X 16 = 256, and the number of elements in z is 4, leading to a total of 1,204 spectral elements. A polynomial order of N = 5 is chosen, and the mesh is generated using the Nek5000 tool genbox. The toolbox presented here allows to compute mean-velocity components, the Reynolds-stress tensor as well as turbulent kinetic energy (TKE) and Reynolds-stress budgets. Note that the present toolbox allows to compute turbulence statistics in turbulent flows with one homogeneous direction (where the statistics are based on time-averaging as well as averaging in the homogeneous direction), as well as in fully three-dimensional flows (with no periodic directions, where only time-averaging is considered).

- Authors:

- KTH Mechanics, Stockholm (Sweden); Swedish e-Science Research Center (SeRC), Stockholm (Sweden)
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1349052

- Report Number(s):
- ANL/MCS-TM-367

133610

- DOE Contract Number:
- AC02-06CH11357

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Vinuesa, Ricardo, Fick, Lambert, Negi, Prabal, Marin, Oana, Merzari, Elia, and Schlatter, Phillip.
```*Turbulence statistics in a spectral element code: a toolbox for High-Fidelity Simulations*. United States: N. p., 2017.
Web. doi:10.2172/1349052.

```
Vinuesa, Ricardo, Fick, Lambert, Negi, Prabal, Marin, Oana, Merzari, Elia, & Schlatter, Phillip.
```*Turbulence statistics in a spectral element code: a toolbox for High-Fidelity Simulations*. United States. doi:10.2172/1349052.

```
Vinuesa, Ricardo, Fick, Lambert, Negi, Prabal, Marin, Oana, Merzari, Elia, and Schlatter, Phillip. Wed .
"Turbulence statistics in a spectral element code: a toolbox for High-Fidelity Simulations". United States.
doi:10.2172/1349052. https://www.osti.gov/servlets/purl/1349052.
```

```
@article{osti_1349052,
```

title = {Turbulence statistics in a spectral element code: a toolbox for High-Fidelity Simulations},

author = {Vinuesa, Ricardo and Fick, Lambert and Negi, Prabal and Marin, Oana and Merzari, Elia and Schlatter, Phillip},

abstractNote = {In the present document we describe a toolbox for the spectral-element code Nek5000, aimed at computing turbulence statistics. The toolbox is presented for a small test case, namely a square duct with Lx = 2h, Ly = 2h and Lz = 4h, where x, y and z are the horizontal, vertical and streamwise directions, respectively. The number of elements in the xy-plane is 16 X 16 = 256, and the number of elements in z is 4, leading to a total of 1,204 spectral elements. A polynomial order of N = 5 is chosen, and the mesh is generated using the Nek5000 tool genbox. The toolbox presented here allows to compute mean-velocity components, the Reynolds-stress tensor as well as turbulent kinetic energy (TKE) and Reynolds-stress budgets. Note that the present toolbox allows to compute turbulence statistics in turbulent flows with one homogeneous direction (where the statistics are based on time-averaging as well as averaging in the homogeneous direction), as well as in fully three-dimensional flows (with no periodic directions, where only time-averaging is considered).},

doi = {10.2172/1349052},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Wed Feb 01 00:00:00 EST 2017},

month = {Wed Feb 01 00:00:00 EST 2017}

}