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.

本文讨论了使用不连续Galerkin方法模拟可压缩，四向耦合，载有颗粒的流的算法的开发。具体来说，算法的发展集中在硬球碰撞的处理上。首先，我们的目标是减少在给定的时间步长上检查粒子对碰撞的计算量。这通常是四向耦合的载有颗粒的流动模拟中最昂贵的阶段之一。所提出的算法利用有关物理粒子到参考元件的几何映射所提供的有关相对粒子位置的信息，这些粒子通常用于不连续的Galerkin和其他基于有限元的求解器中。第二，我们开发了一种增强的粒子-壁碰撞方法，该方法比以前开发的方案更好地说明了有限的粒径。粒子-粒子和粒子-壁碰撞算法的一个特殊功能是与任意，弯曲的，非结构化的元素兼容。最后，我们将结果框架应用于许多测试案例，包括进入舱上方的超音速尘土流和喷砂处理引起的表面腐蚀。