Towards a unified Lagrangian multi‐scale model for interacting particles

Abstract

AbstractThe simulation of interacting particle systems by individual tracking in a Lagrangian framework can become virtually impossible in feasible time frames and for large problem sizes. This is why there are many approaches to describe the resulting behavior by continuous equations which are usually much more efficiently solved using an Eulerian grid on a larger scale. Motivated by the development of a Lagrangian generalized finite difference solver using moving point clouds, we work towards a method that can blend between the different scales in a unified framework. To this end, we derive a macroscopic model which still contains microscopic information in the form of an integral term. Different approximations of this term based on the point cloud configuration shall allow for a scaling between the representation of microscopic particles and the solution of a purely macroscopic model by the point cloud. Here we will present an extension of the model to interacting particle systems that involve damping and focus on the macroscopic model performance.