A massive MPI parallel framework of 3D local discontinuous Galerkin method for simulating large-scale underwater explosion problems

The discontinuous Galerkin method (DGM) has showed appealing performances in addressing underwater explosion (UNDEX) problems with strong discontinuities. However, most of the DGM are limited to the axisymmetric modeling due to the expensive computational cost required in 3D simulations. In this work, we develop a massive MPI parallel framework of 3D local discontinuous Galerkin method (LDGM) for simulating large-scale UNDEX problems with the cavitation effects. The 3D LDGM based on unstructured tetrahedron elements is adopted to solve the wave equation about dynamic pressure excited by the UNDEX and simulate the propagation of the UNDEX shock waves in the fluid domain. To accelerate the calculation of 3D LDGM, the MPI parallel framework scalable on a high-performance computer is designed. In order to improve the parallel efficiency and expand the computational scalability, some optimized techniques are incorporated into the parallel 3D LDGM model. In particular, the information for data communication is stored contiguously in the access-friendly data structures to efficiently implement concurrent non-blocking communications. The real-time memory management strategies with local parallel I/O are developed in terms of reducing latency and restraining memory utilization. Several numerical examples are performed to assess the accuracy, efficiency and scalability of the MPI-based parallel 3D LDGM model. It is demonstrated that the present model can accurately and efficiently simulate the propagation of UNDEX shock waves and well capture the evolution of the cavitation region in 3D spaces. The parallel efficiency can achieve up to 94.1 % even for 155 million tetrahedral elements on 12,000 CPU cores.