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, is 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 is 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.
翻译:本条详细介绍了基于密度的潮流问题优化流体表层图示,目的是让新学生和研究人员能够迅速开始研究领域,跳过许多初步步骤,往往不必要地从该领域的科学进步中耗去很长的时间,往往不必要地耗费了从该领域科学进步到该领域的科学进步的时间。这是通过为理解和实施理论的必要组成部分提供分步指南,以及扩展所提供的 MATLAB 代码来实现的。 讨论了用于模拟液流领域浸泡固体的布林克曼惩罚办法的连续设计说明及其如何与布林克曼惩罚办法相联系。 说明了对布林克曼惩罚条款的不同解释以及如何选择刑罚参数。 布林克曼惩罚办法的准确性是通过参考几何方法的参数模拟加以分析的。 所选定的限定要素的拟订和解决方案方法得到了解释。 最低限度的能源优化问题得到了界定,并讨论了如何使用最佳标准求解和延续办法解决这个问题。 包括MATLAB执行方式,详细记录了布林克曼刑罚的使用情况,并解释了如何选择刑罚参数。 布林克曼惩罚办法的准确性方法,通过参考度模拟模型来分析。 通过参考参考度测算法的参数。 代码,通过测试了两个基准,通过对最后的修改和后算法进行了测试。 标准进行了两次基准,通过这些修改,通过这些修改,通过这些修改。