A two-way coupled Euler-Lagrange method for simulating multiphase flows with discontinuous Galerkin schemes on arbitrary curved elements

Abstract

In this work, we develop a Lagrangian point-particle method to support high-speed dusty flow simulations with discontinuous Galerkin schemes. The carrier fluid is treated in an Eulerian frame through the solution of the compressible Navier-Stokes equations. Particle search and localization is based on the geometric mapping of mesh elements to a reference element and is applicable to arbitrary unstructured, curved, multidimensional grids. High-order interpolation is used to calculate the gas state at a given particle position, and the back-coupling of particles to the carrier fluid is carried out via a simple, effective procedure. Furthermore, we discuss difficulties associated with accounting for particle-wall collisions on curved, high-aspect-ratio elements. We develop a methodology that appropriately handles such collisions and accurately computes post-collision particle trajectories. We first apply the Euler-Lagrange method to one-way coupled tests and show the benefit of using curved instead of straight-sided elements for dealing with particle-wall collisions. We proceed by considering more complex multiphase test cases with two-way coupling, namely dusty flows over a flat plate and through a converging-diverging nozzle. Our final test case consists of hypersonic dusty flow over a sphere in which the target quantity is dust-induced surface heating augmentation at the stagnation point. Quantitative comparisons with experiments are provided.