Pairwise Interaction Model for Coarse-Grained Parcels in Shock-Driven Particle-Laden Flows

Compressible particle-laden flows appear in many natural and engineering systems. Simulating them often relies on the Euler-Lagrange framework, where the fluid is modeled in an Eulerian frame and particles are tracked in a Lagrangian frame. Pairwise interaction point-particle models can capture force variations caused by particle-particle interactions based on neighboring particle positions.

However, tracking every particle becomes too expensive for large-scale simulations. A common approach is to use coarse-grained parcels, where each parcel represents many real particles. This work extends the existing particle pairwise interaction framework to coarse-grained parcels. We derive the parcel-scaled formulation of the Maxey–Riley–Gatignol equations and address the development from particle-based interaction maps to coarse-grained interaction maps, achieving a balance between computational accuracy and cost.