Development of a particle collision algorithm for discontinuous Galerkin simulations of compressible multiphase flows

Abstract

This paper discusses the development of algorithms for simulating compressible, four-way coupled, particle-laden flows with discontinuous Galerkin methods. Specifically, the algorithmic developments focus on the treatment of hard-sphere collisions. First, we aim to reduce the computational effort devoted to inspecting pairs of particles for collisions during the given time step. This is often one of the most expensive stages of four-way coupled particle-laden flow simulations. The proposed algorithm exploits information about relative particle positions provided by the geometric mapping of a physical element to a reference element commonly employed in discontinuous Galerkin and other finite-element-based solvers. Second, we develop an enhanced particle-wall collision methodology that better accounts for finite particle size than previously developed schemes. A particular feature of the particle-particle and particle-wall collision algorithms is compatibility with arbitrary, curved, unstructured elements. Finally, we apply the resulting framework to a number of test cases, including hypersonic dusty flow over an entry capsule and surface erosion by sandblasting.