Direct numerical simulation of the motion of circular pollutant particles in Newtonian fluid

An improved implementation of distributed multiplier/fictitious domain method is presented for the direct numerical simulation of particulate flow. The key improvement is to replace a finite-element triangulation for the velocity and a "twice-coarser" triangulation for the pressure with a rectangular discretization for the velocity and pressure. For code validation, the sedimentation of a single particle in a two-dimensional channel was simulated. The results showed that the simulation is independent of the mesh size as well as the time step. The comparison between experimental data and this simulation showed that our code can give a more accurate simulation on the motion of particles than previous DLM code. The code was then applied to simulate the sedimentation of 600 particles in a rectangular box. The falling course is presented and discussed. At the same time, this simulation also demonstrates that the method presented in this paper can be used for solving the initial problems involving a lager number of particles exactly with computing durations kept at acceptable levels.