Abstract

While students may find spline interpolation quite digestible based on their familiarity with the continuity of a function and its derivatives, some of its inherent value may be missed when they only see it applied to standard data interpolation exercises. In this paper, we offer alternatives in which students can qualitatively and quantitatively witness the resulting dynamical differences when objects are driven through a fluid using different spline interpolation methods. They say that seeing is believing; here we showcase the differences between linear and cubic spline interpolation using examples from fluid pumping and aquatic locomotion. Moreover, students can define their own interpolation functions and visualize the dynamics that unfold. To solve the fluid-structure interaction system, the open-source fluid dynamics software IB2d is used. In that spirit, all simulation codes, analysis scripts, and movies are provided for streamlined use.

Keywords

  1. numerical analysis education
  2. fluid dynamics education
  3. mathematical biology education
  4. immersed boundary method
  5. fluid-structure interaction
  6. biological fluid dynamics

MSC codes

  1. 65D05
  2. 65D07
  3. 97M10
  4. 97M60
  5. 97N40
  6. 97N50
  7. 97N80
  8. 76M25
  9. 76Z10
  10. 76Z99
  11. 92C10

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Supplementary Material


PLEASE NOTE: These supplementary files have not been peer-reviewed.


Index of Supplementary Materials

Title of paper: Fluid-Structure Interaction for the Classroom: Interpolation, Hearts, and Swimming!

Author: Nicholas A. Battista

File: M120928SupMat1.zip

Type: zip file

Contents: Movies and codes pertaining to all the simulations detailed in the manuscript.


File: M120928SupMat2.pdf

Type: PDF

Contents: Specifically indexes what items are included in the Supplemental.zip folder and lists the cubic interpolation coefficients for various cases presented in the text.

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Information & Authors

Information

Published In

cover image SIAM Review
SIAM Review
Pages: 181 - 207
ISSN (online): 1095-7200

History

Submitted: 23 August 2018
Accepted: 2 January 2020
Published online: 4 February 2021

Keywords

  1. numerical analysis education
  2. fluid dynamics education
  3. mathematical biology education
  4. immersed boundary method
  5. fluid-structure interaction
  6. biological fluid dynamics

MSC codes

  1. 65D05
  2. 65D07
  3. 97M10
  4. 97M60
  5. 97N40
  6. 97N50
  7. 97N80
  8. 76M25
  9. 76Z10
  10. 76Z99
  11. 92C10

Authors

Affiliations

Funding Information

TCNJ SOSA
National Science Foundation https://doi.org/10.13039/100000001 : OAC-1828163

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