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Harmonic Balance Techniques in Cardiovascular Fluid Mechanics

by T. S. Koltukluoglu and G. Cvijetic and R. Hiptmair

(Report number 2019-55)

Abstract
In cardiovascular fluid mechanics, the typical flow regime is unsteady and periodic in nature as dictated by cardiac dynamics. Most studies featuring computational simulations have approached the problem exploiting the traditional mathematical formulation in the time domain, an approach that incurs huge computational cost. This work explores the application of the harmonic balance method as an alternative numerical modeling tool to resolve the dynamic nature of blood flow. The method takes advantage of the pulsatile regime to transform the original problem into a family of equations in frequency space, while the combination of the corresponding solutions yields the periodic solution of the original problem. As a result of this study we conclude that only a few harmonics are required for resolving the presented fluid flow problem accurately and the method is worth of further investigation in this field.

Keywords: Harmonic balance, cardiac dynamics, pulsatile blood flow.

@Techreport{KCH19_859,
  author = {T. S. Koltukluoglu and G. Cvijetic and R. Hiptmair},
  title = {Harmonic Balance Techniques in Cardiovascular Fluid Mechanics},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2019-55},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2019/2019-55.pdf },
  year = {2019}
}

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