An Euler-Lagrange formulation for simulating high-speed dusty flows using discontinuous Galerkin schemes

This works presents an Euler-Lagrange formulation for simulating particle-laden flows using discontinuous Galerkin schemes. The method uses a mesoscopic modeling approach in which particles are tracked as point sources while the carrier gas is described using an Eulerian field. We discuss an efficient tracking algorithm that not only locates the host element of a particle for subsequent interpolation of the carrier gas state but also accurately detects particle-wall collisions and computes post-collision trajectories. The algorithm is well-suited for curved, high-aspect-ratio elements. A series of test cases is presented that assesses the accuracy of the method on high-order spatial discretizations. Emphasis is placed on application of the method to investigate surface heat flux augmentation in hypersonic dusty flows over blunt bodies. We examine the importance of various forcing terms, drag correlations, and Nusselt number correlations in the particle momentum and energy equations for these types of flows. Quantitative comparisons with experiments are provided.