# Development of Adaptive Model Refinement (AMoR) for Multiphysics and Multifidelity Problems

## Abstract

This project investigated the development and utilization of Adaptive Model Refinement (AMoR) for nuclear systems simulation applications. AMoR refers to utilization of several models of physical phenomena which differ in prediction fidelity. If the highest fidelity model is judged to always provide or exceeded the desired fidelity, than if one can determine the difference in a Quantity of Interest (QoI) between the highest fidelity model and lower fidelity models, one could utilize the fidelity model that would just provide the magnitude of the QoI desired. Assuming lower fidelity models require less computational resources, in this manner computational efficiency can be realized provided the QoI value can be accurately and efficiently evaluated. This work utilized Generalized Perturbation Theory (GPT) to evaluate the QoI, by convoluting the GPT solution with the residual of the highest fidelity model determined using the solution from lower fidelity models. Specifically, a reactor core neutronics problem and thermal-hydraulics problem were studied to develop and utilize AMoR. The highest fidelity neutronics model was based upon the 3D space-time, two-group, nodal diffusion equations as solved in the NESTLE computer code. Added to the NESTLE code was the ability to determine the time-dependent GPT neutron flux. The lower fidelity neutronicsmore »

- Authors:

- North Carolina State Univ., Raleigh, NC (United States)

- Publication Date:

- Research Org.:
- North Carolina State Univ., Raleigh, NC (United States)

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

- OSTI Identifier:
- 1169938

- Report Number(s):
- 09-793

09-793

- DOE Contract Number:
- AC07-05ID14517

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS

### Citation Formats

```
Turinsky, Paul.
```*Development of Adaptive Model Refinement (AMoR) for Multiphysics and Multifidelity Problems*. United States: N. p., 2015.
Web. doi:10.2172/1169938.

```
Turinsky, Paul.
```*Development of Adaptive Model Refinement (AMoR) for Multiphysics and Multifidelity Problems*. United States. doi:10.2172/1169938.

```
Turinsky, Paul. Mon .
"Development of Adaptive Model Refinement (AMoR) for Multiphysics and Multifidelity Problems". United States.
doi:10.2172/1169938. https://www.osti.gov/servlets/purl/1169938.
```

```
@article{osti_1169938,
```

title = {Development of Adaptive Model Refinement (AMoR) for Multiphysics and Multifidelity Problems},

author = {Turinsky, Paul},

abstractNote = {This project investigated the development and utilization of Adaptive Model Refinement (AMoR) for nuclear systems simulation applications. AMoR refers to utilization of several models of physical phenomena which differ in prediction fidelity. If the highest fidelity model is judged to always provide or exceeded the desired fidelity, than if one can determine the difference in a Quantity of Interest (QoI) between the highest fidelity model and lower fidelity models, one could utilize the fidelity model that would just provide the magnitude of the QoI desired. Assuming lower fidelity models require less computational resources, in this manner computational efficiency can be realized provided the QoI value can be accurately and efficiently evaluated. This work utilized Generalized Perturbation Theory (GPT) to evaluate the QoI, by convoluting the GPT solution with the residual of the highest fidelity model determined using the solution from lower fidelity models. Specifically, a reactor core neutronics problem and thermal-hydraulics problem were studied to develop and utilize AMoR. The highest fidelity neutronics model was based upon the 3D space-time, two-group, nodal diffusion equations as solved in the NESTLE computer code. Added to the NESTLE code was the ability to determine the time-dependent GPT neutron flux. The lower fidelity neutronics model was based upon the point kinetics equations along with utilization of a prolongation operator to determine the 3D space-time, two-group flux. The highest fidelity thermal-hydraulics model was based upon the space-time equations governing fluid flow in a closed channel around a heat generating fuel rod. The Homogenous Equilibrium Mixture (HEM) model was used for the fluid and Finite Difference Method was applied to both the coolant and fuel pin energy conservation equations. The lower fidelity thermal-hydraulic model was based upon the same equations as used for the highest fidelity model but now with coarse spatial meshing, corrected somewhat by employing effective fuel heat conduction values. The effectiveness of switching between the highest fidelity model and lower fidelity model as a function of time was assessed using the neutronics problem. Based upon work completed to date, one concludes that the time switching is effective in annealing out differences between the highest and lower fidelity solutions. The effectiveness of using a lower fidelity GPT solution, along with a prolongation operator, to estimate the QoI was also assessed. The utilization of a lower fidelity GPT solution was done in an attempt to avoid the high computational burden associated with solving for the highest fidelity GPT solution. Based upon work completed to date, one concludes that the lower fidelity adjoint solution is not sufficiently accurate with regard to estimating the QoI; however, a formulation has been revealed that may provide a path for addressing this shortcoming.},

doi = {10.2172/1169938},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Mon Feb 09 00:00:00 EST 2015},

month = {Mon Feb 09 00:00:00 EST 2015}

}