# Development of harmonic balance capability for Charon.

## Abstract

We report on the development of a frequency domain method of analysis in the Panzer foundation of Charon. We first present a harmonic balance approach for calculating the frequency-domain re- sponse (in its weak form) of a non-linear system of partial differential equations (PDEs). Our approach is anemable to adaptation of Charon's transient PDE models for frequency domain analysis. We make an observation that allows us to analyze either small-signal or large-signal responses with minimal specialization of the algorithm. We conclude by confirming our small- and large-signal analyses of a transient, linear Helmholtz equation by comparing its analytic solution to our results. We include figures from a sequence of non-linear perturbations of this system, showcasing the fact that, when the non-linearities are insignificant, the small- and large-signal analyses obtain similar solutions. On the other hand, we depict the inadequacy of a small-signal analysis to accurately capture the response in the presence of a large non-linearity, and underscore the requirement to employ a large-signal analysis for modelling highly non-linear systems.

- Authors:

- Publication Date:

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

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

- OSTI Identifier:
- 1489869

- Report Number(s):
- SAND2018-3623

671158

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Huang, Andy, Huang, Andy, and Huang, Andy.
```*Development of harmonic balance capability for Charon.*. United States: N. p., 2018.
Web. doi:10.2172/1489869.

```
Huang, Andy, Huang, Andy, & Huang, Andy.
```*Development of harmonic balance capability for Charon.*. United States. doi:10.2172/1489869.

```
Huang, Andy, Huang, Andy, and Huang, Andy. Sun .
"Development of harmonic balance capability for Charon.". United States. doi:10.2172/1489869. https://www.osti.gov/servlets/purl/1489869.
```

```
@article{osti_1489869,
```

title = {Development of harmonic balance capability for Charon.},

author = {Huang, Andy and Huang, Andy and Huang, Andy},

abstractNote = {We report on the development of a frequency domain method of analysis in the Panzer foundation of Charon. We first present a harmonic balance approach for calculating the frequency-domain re- sponse (in its weak form) of a non-linear system of partial differential equations (PDEs). Our approach is anemable to adaptation of Charon's transient PDE models for frequency domain analysis. We make an observation that allows us to analyze either small-signal or large-signal responses with minimal specialization of the algorithm. We conclude by confirming our small- and large-signal analyses of a transient, linear Helmholtz equation by comparing its analytic solution to our results. We include figures from a sequence of non-linear perturbations of this system, showcasing the fact that, when the non-linearities are insignificant, the small- and large-signal analyses obtain similar solutions. On the other hand, we depict the inadequacy of a small-signal analysis to accurately capture the response in the presence of a large non-linearity, and underscore the requirement to employ a large-signal analysis for modelling highly non-linear systems.},

doi = {10.2172/1489869},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {4}

}