A detailed introduction to density-based topology optimisation of fluid flow problems with implementation in MATLAB

Joe Alexandersen*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

This article presents a detailed introduction to density-based topology optimisation of fluid flow problems. The goal is to allow new students and researchers to quickly get started in the research area and to skip many of the initial steps, often consuming unnecessarily long time from the scientific advancement of the field. This is achieved by providing a step-by-step guide to the components necessary to understand and implement the theory, as well as extending the supplied MATLAB code. The continuous design representation used and how it is connected to the Brinkman penalty approach, for simulating an immersed solid in a fluid domain, are illustrated. The different interpretations of the Brinkman penalty term and how to chose the penalty parameters are explained. The accuracy of the Brinkman penalty approach is analysed through parametric simulations of a reference geometry. The chosen finite element formulation and the solution method are explained. The minimum dissipated energy optimisation problem is defined and how to solve it using an optimality criteria solver and a continuation scheme is discussed. The included MATLAB implementation is documented, with details on the mesh, pre-processing, optimisation and post-processing. The code has two benchmark examples implemented and the application of the code to these is reviewed. Subsequently, several modifications to the code for more complicated examples are presented through provided code modifications and explanations. Lastly, the computational performance of the code is examined through studies of the computational time and memory usage, along with recommendations to decrease computational time through approximations.

Original languageEnglish
Article number12
JournalStructural and Multidisciplinary Optimization
Volume66
Issue number1
Number of pages38
ISSN1615-147X
DOIs
Publication statusPublished - Jan 2023

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

  • Education
  • Fluid flow
  • MATLAB
  • Topology optimisation

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