Convergence of Point Particle Models in Euler-Lagrange Simulations of Shock-Particle Interaction

Point particle methods are extensively used in simulating Euler-Lagrange multiphase dispersed flow. However, numerical convergence and accuracy of these methods under mesh refinement is still an open question. The standard approach of approximating the fluid-particle coupling at the particle center fails to converge as the Eulerian grid is reduced below particle size. To quantify the spatial discretization error, we consider the Faxèn form of the coupling between the particle and the fluid to account for the finite size of the particle and demonstrate this approach permits convergence. The generalized Faxén form also allows for apportioning of the different force components to fluid cells based on the fraction of particle volume or the fraction of particle surface area in the cell. We tested this approach on a four-way coupled one-dimensional model of shock propagation through a particle-laden field at moderate volume fraction, where the convergence is achieved for a well-formulated force model and back coupling for finite size particles.