# Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

## Abstract

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

- Authors:

- Sandia National Laboratories, Computational Mathematics Department (United States)
- (United States)
- Sandia National Laboratories, Multiphysics Applications Department (United States)
- Sandia National Laboratories, Optimization and UQ Department (United States)

- Publication Date:

- OSTI Identifier:
- 22572348

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 321; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ERRORS; FLUID FLOW; HEAT TRANSFER; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; NAVIER-STOKES EQUATIONS; REACTORS; REYNOLDS NUMBER; SENSITIVITY; SIMULATION; THERMAL HYDRAULICS

### Citation Formats

```
Shadid, J.N., E-mail: jnshadi@sandia.gov, Department of Mathematics and Statistics, University of New Mexico, Smith, T.M., Cyr, E.C., Wildey, T.M., and Pawlowski, R.P.
```*Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities*. United States: N. p., 2016.
Web. doi:10.1016/J.JCP.2016.04.062.

```
Shadid, J.N., E-mail: jnshadi@sandia.gov, Department of Mathematics and Statistics, University of New Mexico, Smith, T.M., Cyr, E.C., Wildey, T.M., & Pawlowski, R.P.
```*Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities*. United States. doi:10.1016/J.JCP.2016.04.062.

```
Shadid, J.N., E-mail: jnshadi@sandia.gov, Department of Mathematics and Statistics, University of New Mexico, Smith, T.M., Cyr, E.C., Wildey, T.M., and Pawlowski, R.P. Thu .
"Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities". United States. doi:10.1016/J.JCP.2016.04.062.
```

```
@article{osti_22572348,
```

title = {Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities},

author = {Shadid, J.N., E-mail: jnshadi@sandia.gov and Department of Mathematics and Statistics, University of New Mexico and Smith, T.M. and Cyr, E.C. and Wildey, T.M. and Pawlowski, R.P.},

abstractNote = {A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.},

doi = {10.1016/J.JCP.2016.04.062},

journal = {Journal of Computational Physics},

number = ,

volume = 321,

place = {United States},

year = {Thu Sep 15 00:00:00 EDT 2016},

month = {Thu Sep 15 00:00:00 EDT 2016}

}