## This content will become publicly available on October 2, 2020

# Bi-fidelity approximation for uncertainty quantification and sensitivity analysis of irradiated particle-laden turbulence

## Abstract

Particle-laden turbulent flows subject to radiative heating are relevant in many applications, for example concentrated solar power receivers. Efficient and accurate simulations provide valuable insights and enable optimization of such systems. However, as there are many uncertainties inherent in such flows, uncertainty quantification is fundamental to improve the predictive capabilities of the numerical simulations. For large-scale, multi-physics problems exhibiting high-dimensional uncertainty, characterizing the stochastic solution presents a significant computational challenge as most strategies require a large number of high-fidelity solves. This requirement might result in an infeasible number of simulations when a typical converged high-fidelity simulation requires intensive computational resources. To reduce the cost of quantifying high-dimensional uncertainties, we investigate the application of a non-intrusive, bi-fidelity approximation to estimate statistics of quantities of interest associated with an irradiated particle-laden turbulent flow. This method exploits the low-rank structure of the solution to accelerate the stochastic sampling and approximation processes by means of cheaper-to-run, lower fidelity representations. Here, the application of this bi-fidelity approximation results in accurate estimates of the quantities of interest statistics, while requiring a small number of high-fidelity model evaluations.

- Authors:

- Univ. of Colorado, Boulder, CO (United States). Applied Mathematics and Statistics; Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
- Stanford Univ., Stanford, CA (United States). Center for Turbulence Research
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
- Univ. of Colorado, Boulder, CO (United States). Smead Aerospace Engineering Sciences

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1574442

- Report Number(s):
- SAND-2019-12147J

Journal ID: ISSN 0021-9991; 680173

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Name: Journal of Computational Physics; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Bi-fidelity approximation; Irradiated particle-laden turbulence; Low-rank approximation; Non-intrusive; Predictive computational science; Uncertainty quantification

### Citation Formats

```
Fairbanks, Hillary R., Jofre, Lluís, Geraci, Gianluca, Iaccarino, Gianluca, and Doostan, Alireza. Bi-fidelity approximation for uncertainty quantification and sensitivity analysis of irradiated particle-laden turbulence. United States: N. p., 2019.
Web. doi:10.1016/j.jcp.2019.108996.
```

```
Fairbanks, Hillary R., Jofre, Lluís, Geraci, Gianluca, Iaccarino, Gianluca, & Doostan, Alireza. Bi-fidelity approximation for uncertainty quantification and sensitivity analysis of irradiated particle-laden turbulence. United States. doi:10.1016/j.jcp.2019.108996.
```

```
Fairbanks, Hillary R., Jofre, Lluís, Geraci, Gianluca, Iaccarino, Gianluca, and Doostan, Alireza. Wed .
"Bi-fidelity approximation for uncertainty quantification and sensitivity analysis of irradiated particle-laden turbulence". United States. doi:10.1016/j.jcp.2019.108996.
```

```
@article{osti_1574442,
```

title = {Bi-fidelity approximation for uncertainty quantification and sensitivity analysis of irradiated particle-laden turbulence},

author = {Fairbanks, Hillary R. and Jofre, Lluís and Geraci, Gianluca and Iaccarino, Gianluca and Doostan, Alireza},

abstractNote = {Particle-laden turbulent flows subject to radiative heating are relevant in many applications, for example concentrated solar power receivers. Efficient and accurate simulations provide valuable insights and enable optimization of such systems. However, as there are many uncertainties inherent in such flows, uncertainty quantification is fundamental to improve the predictive capabilities of the numerical simulations. For large-scale, multi-physics problems exhibiting high-dimensional uncertainty, characterizing the stochastic solution presents a significant computational challenge as most strategies require a large number of high-fidelity solves. This requirement might result in an infeasible number of simulations when a typical converged high-fidelity simulation requires intensive computational resources. To reduce the cost of quantifying high-dimensional uncertainties, we investigate the application of a non-intrusive, bi-fidelity approximation to estimate statistics of quantities of interest associated with an irradiated particle-laden turbulent flow. This method exploits the low-rank structure of the solution to accelerate the stochastic sampling and approximation processes by means of cheaper-to-run, lower fidelity representations. Here, the application of this bi-fidelity approximation results in accurate estimates of the quantities of interest statistics, while requiring a small number of high-fidelity model evaluations.},

doi = {10.1016/j.jcp.2019.108996},

journal = {Journal of Computational Physics},

number = ,

volume = ,

place = {United States},

year = {2019},

month = {10}

}