A novel Euler-Lagrange method that incorporates fully resolved physics using pairwise interaction extended point-particle (PIEP) model.

In the traditional Euler-Lagrange (EL) method the point-particle (PP) force models are based on flow Reynolds number and local particle volume fraction as seen by the particle. The presence of neighboring particles is only taken into account on average through the local particle volume fraction. Here we start with the complete N-particle problem and employ pairwise-interaction and order-invariance assumptions to rigorously simplify the problem and develop a new framework of pairwise interaction extended point-particle (PIEP) approach for coupling the particulate and fluid phases. The key ingredient in this approach is axisymmetric maps of perturbation effects of a neighbor, which can be thought of as richer drag/lift laws. We will discuss how machine learning can be used, guided by physical understanding, to develop these maps from the DNS data of flow over a random array of particles.