A MATLAB topology optimization code to control the trajectory of particle in fluid

Abstract

This paper presents an educational code for topology optimization controlling the trajectory of particle in steady-state laminar fluid. To control the trajectory of particle, fluid motion is optimized by the fluid topology optimization. The one-way forward analysis between fluid and particle and the adjoint sensitivity analysis are formulated and implemented in the framework of MATLAB. The Navier-Stokes equation is solved by the finite element method with Newton-Raphson iteration and Newton's equation for the analysis of transient particle motion is solved by the Newmark scheme. In the present paper, the educational code is attached in the supplementary material. Throughout the code, the optimization problems considering particle trajectory can be solved. The code consists of the finite element analysis of a fluid, transient analysis of a particle suspended in fluid, and computation of the adjoint sensitivity analysis. This code can be easily expanded for complex particle fluid problems. Several benchmark problems are presented that control the velocity and position of a particle and separate multiple particles suspended in a fluid.