Title: Efficient computation of particle-fluid and particle-particle interactions in compressible flow Show Chinese title

Title: 可压缩流中粒子-流体和粒子-粒子相互作用的高效计算

Abstract: Particle collisions are the primary mechanism of inter-particle momentum and energy exchange for dense particle-laden flow. Accurate approximation of this collision operator in four-way coupled Euler-Lagrange approaches remains challenging due to the associated computational cost. Adopting a deterministic collision model and a hard-sphere approach eases time step constraints but imposes non-locality on distributed memory architectures, necessitating the inclusion of collision partners from each grid element in the vicinity. Retaining high-order accuracy and parallel efficiency also ties into the correct and compact treatment of the particle-fluid coupling, where adequate kernels are required to effectively project the work of the particles to the Eulerian grid. In this work, we present an efficient particle collision and projection operator based on an MPI+MPI hybrid approach to enable time-resolved and high-order accurate simulations of compressible, four-way coupled particle-laden flows at dense concentrations. A distinct feature of the proposed particle collision algorithm is the efficient calculation of exact binary inter-particle collisions on arbitrary core counts. Combining the particle operator with a hybrid discretization operator based on a high-order discontinuous Galerkin method and a localized low-order finite volume operator allows an accurate treatment of highly compressible particle-laden flows. The approach is extensively validated against a range of benchmark problems. Contrary to literature, the scaling properties are demonstrated on state-of-the-art high performance computing systems. Finally, the proposed algorithm is compatible with unstructured, curved high-order grids which permits the handling of complex geometries as is emphasized by application of the framework to large-scale application cases. Show Chinese abstract

Abstract: 粒子碰撞是密集颗粒载流中颗粒间动量和能量交换的主要机制。 在四向耦合的欧拉-拉格朗日方法中，对这种碰撞算子的准确近似仍然具有挑战性，这是由于相关的计算成本较高。 采用确定性碰撞模型和硬球方法可以缓解时间步长的约束，但在分布式内存架构上会引入非局部性，需要将每个网格单元附近的碰撞伙伴包含进来。 保持高阶精度和平行效率也与正确的和紧凑的颗粒-流体耦合处理有关，其中需要适当的核函数来有效地将颗粒的工作投影到欧拉网格上。 在本工作中，我们提出了一种基于MPI+MPI混合方法的高效粒子碰撞和投影算子，以实现对高密度下可压缩的四向耦合颗粒载流的时间分辨和高阶精确模拟。 所提出的粒子碰撞算法的一个显著特点是能够在任意核心数量上高效计算精确的二元颗粒间碰撞。 将粒子算子与基于高阶不连续伽辽金方法和局部低阶有限体积算子的混合离散化算子相结合，可以准确处理高度可压缩的颗粒载流。 该方法经过了多种基准问题的广泛验证。 与文献不同，该方法的扩展特性是在最先进的高性能计算系统上进行演示的。 最后，所提出的算法兼容非结构化、曲面高阶网格，这使得能够处理复杂几何结构，如框架应用于大规模应用案例时所强调的那样。