# EFFECT OF DISCRETIZATION ERROR ON THE QUANTIFICATION OF MODEL UNCERTAINTY IN TWO-PHASE FLOW SIMULATIONS

## Abstract

Verification, validation and uncertainty quantification (VVUQ) have become a common practice in thermal-hydraulics analysis. In general, these activities deal with propagations of uncertainties in computer code simulations, e.g., through system analysis codes. However, most existing such activities in thermal-hydraulics analysis have been primarily focused on input and model uncertainties, while numerical errors were largely overlooked. Numerical errors can appear in many different forms, e.g., round-off error, statistical sampling error, and discretization error. In thermal-hydraulics analysis, especially two-phase flow simulations commonly encountered in reactor safety analysis, the lack of consideration of discretization error is mainly due to the difficulty in estimating them. Accurate estimations of discretization error require continuous mesh refinement and/or implementation of high-order numerical schemes in system analysis code, both of which are difficult to achieve in existing codes. In this work, we will build a computer code that incorporates both first-order and second-order numerical methods to solve the two-phase flow problems. The first-order method resembles the one used in many existing system analysis codes; and the second-order method works as the reference to estimate numerical errors. Numerical verification of spatial discretization schemes will be presented in the form of mesh convergence study. It will also be demonstrated viamore »

- Authors:

- Idaho National Laboratory
- University of Illinois at Urbana-Champaign

- Publication Date:

- Research Org.:
- Idaho National Lab. (INL), Idaho Falls, ID (United States)

- Sponsoring Org.:
- USDOE Office of Nuclear Energy (NE)

- OSTI Identifier:
- 1478767

- Report Number(s):
- INL/CON-17-43689-Rev000

- DOE Contract Number:
- AC07-05ID14517

- Resource Type:
- Conference

- Resource Relation:
- Conference: ANS International Conference on Best-Estimate Plus Uncertainties Methods (BEPU-2018), Lucca, Italy, 05/13/2018 - 05/18/2018

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 - ENGINEERING; 97 - MATHEMATICS AND COMPUTING; Two-phase flow; discretization error; uncertainty quantification

### Citation Formats

```
Zou, Ling, Kozlowski, Tomasz, and Hu, Guojun.
```*EFFECT OF DISCRETIZATION ERROR ON THE QUANTIFICATION OF MODEL UNCERTAINTY IN TWO-PHASE FLOW SIMULATIONS*. United States: N. p., 2018.
Web.

```
Zou, Ling, Kozlowski, Tomasz, & Hu, Guojun.
```*EFFECT OF DISCRETIZATION ERROR ON THE QUANTIFICATION OF MODEL UNCERTAINTY IN TWO-PHASE FLOW SIMULATIONS*. United States.

```
Zou, Ling, Kozlowski, Tomasz, and Hu, Guojun. Tue .
"EFFECT OF DISCRETIZATION ERROR ON THE QUANTIFICATION OF MODEL UNCERTAINTY IN TWO-PHASE FLOW SIMULATIONS". United States. https://www.osti.gov/servlets/purl/1478767.
```

```
@article{osti_1478767,
```

title = {EFFECT OF DISCRETIZATION ERROR ON THE QUANTIFICATION OF MODEL UNCERTAINTY IN TWO-PHASE FLOW SIMULATIONS},

author = {Zou, Ling and Kozlowski, Tomasz and Hu, Guojun},

abstractNote = {Verification, validation and uncertainty quantification (VVUQ) have become a common practice in thermal-hydraulics analysis. In general, these activities deal with propagations of uncertainties in computer code simulations, e.g., through system analysis codes. However, most existing such activities in thermal-hydraulics analysis have been primarily focused on input and model uncertainties, while numerical errors were largely overlooked. Numerical errors can appear in many different forms, e.g., round-off error, statistical sampling error, and discretization error. In thermal-hydraulics analysis, especially two-phase flow simulations commonly encountered in reactor safety analysis, the lack of consideration of discretization error is mainly due to the difficulty in estimating them. Accurate estimations of discretization error require continuous mesh refinement and/or implementation of high-order numerical schemes in system analysis code, both of which are difficult to achieve in existing codes. In this work, we will build a computer code that incorporates both first-order and second-order numerical methods to solve the two-phase flow problems. The first-order method resembles the one used in many existing system analysis codes; and the second-order method works as the reference to estimate numerical errors. Numerical verification of spatial discretization schemes will be presented in the form of mesh convergence study. It will also be demonstrated via case studies that, in practical scenarios, discretization errors can be as large as, or even larger than, model uncertainties.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {5}

}