Coarse-graining Algorithms for the Eulerian-Lagrangian Simulation of Particle-laden Flows

TL;DR

This paper introduces novel coarse-graining algorithms, including variants of RKPM and an extended DTSM, to improve the accuracy and robustness of Eulerian-Lagrangian simulations of particle-laden flows, with thorough benchmarking and analysis.

Contribution

It proposes new coarse-graining algorithms for EL simulations, combining high-order RKPM variants with hybrid approaches for enhanced accuracy and robustness.

Findings

First-order RKPM outperforms others in accuracy and properties.

Extended DTSM offers a computationally affordable alternative.

Algorithms are validated through benchmarks and grid tests.

Abstract

In the present article, novel Coarse-Graining (CG) algorithms for the Eulerian-Lagrangian (EL) simulation of particle-laden flows are proposed. These include different variants of Reproducing Kernel Particle Methods (RKPM) and an extended Diffusion Two-Step Method (DTSM) for highly polydisperse flows. Owing to the dynamic nature of the kernel function in RKPMs, CG algorithms with high-order consistency properties are constructed and the extra physics of the fluid-particle interaction torque effect on the two-way coupling force distributed to the fluid is taken into consideration. To increase the robustness of RKPMs, they are hybridized with other simple CG algorithms in such a way that each model is activated in the range of its validity. The performance of the new CG algorithms is carefully assessed in comparison to other widely-used algorithms by devising four benchmarks and several grid-independence tests. Based on the analyses, the first-order RKPM demonstrates the best performance in terms of 8 attributes, including conservativity, grid-independency, smoothness, etc., among all algorithms and is recommended when the accuracy is of prime importance. However, due to its higher computational cost compared to the extended DTSM, the latter model would be an affordable alternative for large-scale discrete element method problems when the computational cost is critical.