Passive concentration dynamics incorporated into the library IB2d, a two-dimensional implementation of the immersed boundary method

Matea Santiago, Nicholas A. Battista, Laura A. Miller, Shilpa Khatri

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we present an open-source software library that can be used to numerically simulate the advection and diffusion of a chemical concentration or heat density in a viscous fluid where a moving, elastic boundary drives the fluid and acts as a source or sink. The fully-coupled fluid-structure interaction problem of an elastic boundary in a viscous fluid is solved using Peskin's immersed boundary method. The addition or removal of the concentration or heat density from the boundary is solved using an immersed boundary-like approach in which the concentration is spread from the immersed boundary to the fluid using a regularized delta function. The concentration or density over time is then described by the advection-diffusion equation and numerically solved. This functionality has been added to our software library, IB2d, which provides an easy-to-use immersed boundary method in two dimensions with full implementations in MATLAB and Python. We provide four examples that illustrate the usefulness of the method. A simple rubber band that resists stretching and absorbs and releases a chemical concentration is simulated as a first example. Complete convergence results are presented for this benchmark case. Three more biological examples are presented: (1) an oscillating row of cylinders, representative of an idealized appendage used for filter-feeding or sniffing, (2) an oscillating plate in a background flow is considered to study the case of heat dissipation in a vibrating leaf, and (3) a simplified model of a pulsing soft coral where carbon dioxide is taken up and oxygen is released as a byproduct from the moving tentacles. This method is applicable to a broad range of problems in the life sciences, including chemical sensing by antennae, heat dissipation in plants and other structures, the advection-diffusion of morphogens during development, filter-feeding by marine organisms, and the release of waste products from organisms in flows.

Original languageEnglish (US)
Article number036003
JournalBioinspiration and Biomimetics
Volume17
Issue number3
DOIs
StatePublished - May 2022

Keywords

  • advection-diffusion
  • biofluids
  • biomechanics
  • fluid-structure interaction
  • immersed boundary method
  • mathematical biology

ASJC Scopus subject areas

  • Biotechnology
  • Biophysics
  • Biochemistry
  • Molecular Medicine
  • Engineering (miscellaneous)

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