Massively-parallel, distributed-memory algorithms for the Lagrangian particle hydrodynamic method [R. Samulyak, X. Wang, H.-C. Chen, Lagrangian particle method for compressible fluid dynamics, J. Comput. Phys., 362 (2018), 1-19] have been developed, verified, and implemented. The key component of parallel algorithms is a particle management module that includes a parallel construction of octree databases, dynamic adaptation and refinement of octrees, and particle migration between parallel subdomains. The particle management module is based on the p4est (parallel forest of k-trees) library. The massively-parallel Lagrangian particle code has been applied to a variety of fundamental science and applied problems. A summary of Lagrangian particle code applications to the injection of impurities into thermonuclear fusion devices and to the simulation of supersonic hydrogen jets in support of laser-plasma wakefield acceleration projects has also been presented.

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