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

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 scientifi...

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Vydáno v:Structural and multidisciplinary optimization Ročník 66; číslo 1; s. 12
Hlavní autor: Alexandersen, Joe
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2023
Springer Nature B.V
Témata:
Computational efficiency
Computational Mathematics and Numerical Analysis
Computing time
Density
Educational Paper
Engineering
Engineering Design
Finite element method
Flow-driven Multiphysics
Fluid dynamics
Fluid flow
Homogenization
Matlab
Methods
Optimality criteria
Theoretical and Applied Mechanics
Topology optimization
Topology optimisation
Education
MATLAB
Fluid flow
ISSN:1615-147X, 1615-1488
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Shrnutí: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.
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ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-022-03420-9