A new framework for the Harmonic Balance Method in OpenFOAM

Stefano Oliani, Nicola Casari, Mauro Carnevale

Research output: Contribution to journalArticlepeer-review

3 Citations (SciVal)


The Harmonic Balance Method is one of the most commonly employed Reduced Order Models for turbomachinery calculations, since it leverages the signal sparsity in the frequency domain to cast the transient equations into a coupled set of steady-state ones. The present work aims at detailing the development and validation of a new framework for the application of the Harmonic Balance Method in the open-source software OpenFOAM. The paper is conceptually divided into building blocks for the implementation of the code. For each of these, theoretical notions and coding strategies are given, and an ad hoc validation test case is presented. This structure has been chosen with the aim of easing the reader in the understanding and implementation of such a method in a generic fluid dynamics solver. In a fully open source philosophy, the library files are freely accessible in the authors’ repository (link provided below in the text).

Original languageEnglish
Article number279
Issue number4
Early online date14 Apr 2022
Publication statusPublished - 30 Apr 2022


  • OpenFOAM
  • compressible flows
  • fourier series
  • harmonic balance
  • spectral methods
  • turbomachinery

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science (miscellaneous)
  • Mechanical Engineering
  • Control and Optimization
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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